# Infinite Series

### Topic Page

Infinite Series### Questions

- What are some examples of infinite series?
- Can an infinite series have a sum?
- What are some examples of convergent series?
- What are common mistakes students make with infinite series?
- How do I use an infinite series to find an approximation for pi?
- How do I find the sum of the infinite series 1 + #1/5# + #1/25# +... ?
- How do I find the sum of the infinite series #1/2# + 1 + 2 + 4 +... ?
- What are some examples of divergent series?
- How do you find the sum of the infinite geometric series 1/2+1/4+1/8+1/16..?
- How do you find the sum of the infinite geometric series 3-1+1/3...?
- How do you find the sum of the infinite geometric series 3 + 1 + 1/3 + 1/9 + ...?
- How do you find the sum of the infinite geometric series 8 - 10 + 12.5 - 15.625 + ...?
- How do you find the sum of the infinite geometric series 215 - 86 + 34.4 - 13.76 + ...?
- How do you find the sum of the infinite geometric series 3 - 2 + 4/3 - 8/9 + ...?
- How do you find the sum of the infinite geometric series -25 - 30 - 36 - 43.2 ...?
- How do you find the sum of the infinite geometric series 9+6+4+...?
- How do you find the sum of the infinite geometric series 18,12,8,...?
- How do you find the sum of the infinite geometric series 12+4+4/3+...?
- How do you find the sum of the infinite geometric series 8+4+2+...?
- How do you find the sum of the infinite geometric series 1+ 3/5+9/25+37/125+........?
- How do you find the sum of the infinite geometric series 80+40+20+...?
- How do you find the sum of the infinite geometric series 2+2/3+2/9+2/27+...?
- How do you find the sum of the infinite geometric series 1, 5, -25, 125,…?
- How do you find the sum of the infinite geometric series 4, 16, 64, 256, 1024...?
- How do you find the sum of the infinite geometric series 14-7+7/2-7/4+....?
- How do you find the sum of the infinite geometric series 8 + 4 + 2 + 1 +...?
- How do you find the sum of the infinite geometric series -2+1-1/2+...?
- How do you find the sum of the infinite geometric series 4-1+1/4-1/16+...?
- How do you find the sum of the infinite geometric series 7 + 28/5 + 112/25 + 448/125?
- How do you find the sum of the infinite geometric series 50 + 125/2 + 625/8 + 3125/32?
- How do you find the sum of the infinite geometric series 4 + 3 + 2.25 + 1.6875 +… ?
- How do you find the sum of the infinite geometric series 1/2 + 1/10+ 1/50+ 1/250+ ... ?
- How do you find the sum of the infinite geometric series 1 + 1/3 + 1/9 + ....?
- How do you find the sum of the infinite geometric series #(1 - x) + (x^3 – x^4) + (x^6 – x^7) + ….. + [x^(3n) - x^(3n+1)] #?
- How do you find the sum of the infinite geometric series 32. 30 + 22.5 + 16.875 + . . . ?
- How do you find the sum of the infinite geometric series 15 - 3 + 0.6 - 0.12 + . . .?
- How do you find the sum of the infinite geometric series 12 + 6 + 3 + . . . ?
- How do you find the sum of the infinite geometric series 4 - 2 + 1 – 1/2 + . . .?
- How do you find the sum of the infinite geometric series -13and1/2 + 9 – 6 + . . . ?
- How do you find the sum of the infinite geometric series -5 – 5/2 – 5/4 - . . .?
- How do you find the sum of the infinite geometric series #4(1/3)^(n - 1)#?
- How do you find the sum of the infinite geometric series #-3(3/4)^(n - 1)#?
- How do you find the sum of the infinite geometric series #1.1(0.5)^(n - 1)#?
- How do you find the sum of the infinite geometric series #12(-1/4)^(n - 1)#?
- How do you find the sum of the infinite geometric series #-2.5(-0.1)^(n - 1)#?
- How do you find the sum of the infinite geometric series 1/5+1/10+1/20+1/40+...?
- How do you find the sum of the infinite geometric series 1+0.1+0.01...?
- How do you find the sum of the infinite geometric series 1/3 + 4/9 + 16/27 + 64/81?
- How do you find the sum of the infinite geometric series 0.9 + 0.09 + 0.009 +…?
- How do you find the sum of the infinite geometric series 1 + 2 + 4 + 8 +… ?
- How do you find the sum of the infinite geometric series -2 + -10 + -50 + -250 +…?
- How do you find the sum of the infinite geometric series 72 + 12 + 2 + +… ?
- How do you find the sum of the infinite geometric series 2 + 1.5 + 1.125 + 0.8437 +…?
- How do you find the sum of the infinite geometric series 405 + 270 + 180...?
- How do you find the sum of the infinite geometric series 1+1/5+1/25+....?
- How do you find the sum of the infinite geometric series 100+90+81+72.9+65.61...?
- How do you find the sum of the infinite geometric series #1/sqrt3 + 1/3 + 1/(3sqrt3) + 1/9 + ...#?
- How do you find the sum of the infinite geometric series #10(2/3)^n# when n=2?
- How do you find the sum of the infinite geometric series 5 + 5/3 + 5/9 + 5/27 +....?
- How do you find the sum of the infinite geometric series 4+2+0-2...?
- How do you find the sum of the infinite geometric series 27+9+3+1+...?
- How do you find the sum of the infinite geometric series 1/4 + 1/8 + 1/16 + 1/32 + ..?
- How do you find the sum of the infinite geometric series 1/7 + 1/28 + 1/112 + 1/448 + ...?
- How do you find the sum of the infinite geometric series 2/3 - 4/9 + 8/27 - 16/81 +...?
- How do you find the sum of the infinite geometric series 1-(1/3) + (1/9) - (1/27) + .....?
- How do you find the sum of the infinite geometric series 1.02 + 2.04 + 4.08 + 8.16 +…?
- How do you find the sum of the infinite geometric series 4 + 3 + 9/4 + ...?
- ?How do you find the sum of the infinite geometric series 4+2+1+1/2+1/4 ...
- ?How do you find the sum of the infinite geometric series 2,9,27,81..?
- ?How do you find the sum of the infinite geometric series 4 + 0.4 + 0.04 + ....?
- ?How do you find the sum of the infinite geometric series 4, 7, 12.25, 21.4375 …?
- ?How do you find the sum of the infinite geometric series 4 + 3.2 + 2.56 + 2.048 + …?
- ?How do you find the sum of the infinite geometric series #2^n/5^(2n+1)#?
- ?How do you find the sum of the infinite geometric series # 6^n/7^n#?
- ?How do you find the sum of the infinite geometric series a1 = 27 and r = -4/5?
- ?How do you find the sum of the infinite geometric series 343+49+7+...?
- ?How do you find the sum of the infinite geometric series #1 - x + x^2 - x^3 + x^4 ...#?
- ?How do you find the sum of the infinite geometric series 0.03, 0.03, 0.003?
- How do you find the sum of the infinite geometric series 7/8 + 7/12 + 7/18 + 7/27 ...?
- How do you find the sum of the infinite geometric series a1=35 r=2/7?
- How do you find the sum of the infinite geometric series 18-6+2-...?
- How do you find the sum of the infinite geometric series #4/25+2/5+1+...# ?
- How do you find the sum of the infinite geometric series 1/8-1/16+1/32-1/64+...?
- How do you find the sum of the infinite geometric series 36+24+16+...?
- How do you find the sum of the infinite geometric series a1=26 and r=1/2?
- How do you find the sum of the infinite geometric series 60 + 84 + 117.6 + 164.64 +…?
- How do you find the sum of the infinite geometric series t1=5 and r = -2?
- How do you find the sum of the infinite geometric series a1 = 42 and r = 6/5?
- How do you find the sum of the infinite geometric series 5+5/6+5/6^2+5/6^3+...?
- How do you find the sum of the infinite geometric series 3-1+1/3-1/9+...?
- How do you find the sum of the infinite geometric series 8 - 4 + 2 - 1 + 1/2 -...?
- How do you find the sum of the infinite geometric series a1= 343, r=7, and a4= -1?
- How do you find the sum of the infinite geometric series 6 + 24 + 96 + 384 +...?
- How do you find the sum of the infinite geometric series 1-1/2+1/4+1/8?
- How do you find the sum of the infinite geometric series 6+5+(25/6)+....?
- How do you find the sum of the infinite geometric series 64,-16,4,-1....?
- How do you find the sum of the infinite geometric series -10,-5,-5/2?
- How do you find the sum of the infinite geometric series 1/2 - 1/6 + 1/18 - ...?
- How do you find the sum of the infinite geometric series 4/5+4/15+4/45...?
- How do you find the sum of the infinite geometric series 2+2/5+2/25+2/125+...?
- How do you find the sum of the infinite geometric series 16 + 24 + ... + 81 + 121.5?
- How do you find the sum of the infinite geometric series -3, -3/2, -3/4, -3/8?
- How do you find the sum of the infinite geometric series (1/4)+(1/10)+(1/18)+(1/28)+(1/40)+...?
- How do you find the sum of the infinite geometric series 4, 1, 1/4, ...?
- How do you find the sum of the infinite geometric series (3/2)-(5/6)+(7/18)-...?
- How do you find the sum of the infinite geometric series 1 - 1/5 + 1/25 - 1/125 + ...?
- How do you find the sum of the infinite geometric series 256+192+144+108...?
- How do you find the sum of the infinite geometric series 0.5 + 0.05 + 0.005 + ...?
- How do you find the sum of the infinite geometric series #(2/9)^2 - (2/9)^3 + (2/9)^4 - (2/9)^5 + ......#?
- How do you find the sum of the infinite geometric series 7+6+(36/7)+(216/49)+...?
- How do you find the sum of the infinite geometric series 2-2+2-2+..?
- How do you find the sum of the infinite geometric series 1/3+1/9+1/27+1/81+...?
- How do you find the sum of the infinite geometric series 5/4-1/4+1/20-1/100+...?
- How do you find the sum of the infinite geometric series 7 + 21 + 63 + 189 + . . .?
- How do you find the sum of the infinite geometric series 3 – 12 + 48 – 192 + …?
- How do you find the sum of the infinite geometric series 1-2+4-..+1024?
- How do you find the sum of the infinite geometric series 2/9+2/27+2/81+2/243+...?
- How do you find the sum of the infinite geometric series 1 + 0.4 + 0.16 + 0.064 + . . .?
- What is the sum of the infinite geometric series 3 + 1 + 1/3 + 1/9 + ...?
- What is the sum of the infinite geometric series 2+2/3+2/9+2/27+...?
- What is the sum of the infinite geometric series 3-1+1/3...?
- What is the sum of the infinite geometric series 9+6+4+...?
- How do you find 4-sd rounded approximation(s) to the solution(s) of #e^x-1/x=pi#?
- How do you find the sum of the infinite geometric series given #a_1=36# and r=2/3?
- How do you find the sum of the infinite geometric series given #a_1=18# and r=-1.5?
- How do you find the sum of the infinite geometric series given #16+24+36+...#?
- How do you find the sum of the infinite geometric series given #1/4+1/6+2/18+ ...#?
- How do you find the sum of the infinite geometric series given #6-2.4+0.96-...#?
- How do you find the sum of the infinite geometric series given #Sigma 40(3/5)^(n-1)# for n=1 to #oo#?
- How do you write the repeating decimal 0.5 as a fraction?
- How do you write the repeating decimal 0.73 where 73 is repeated as a fraction?
- How do you write the repeating decimal 0.175 where 175 is repeated as a fraction?
- How do you find the sum of the infinite geometric series given #a_1=4# and r=5/7?
- How do you find the sum of the infinite geometric series given #a_1=14#, r=7/3?
- How do you find the sum of the infinite geometric series given #a_1=12#, r=-0.6?
- How do you find the sum of the infinite geometric series given #a_1=18# and r=0.6?
- How do you find the sum of the infinite geometric series given #16+12+9+...#?
- How do you find the sum of the infinite geometric series given #-8-4-2-...#?
- How do you find the sum of the infinite geometric series given #12-18+24-...#?
- How do you find the sum of the infinite geometric series given #18-12+8-...#?
- How do you find the sum of the infinite geometric series given #1+2/3+4/9+...#?
- How do you find the sum of the infinite geometric series given #5/3+25/3+125/3+...#?
- How do you find the sum of the infinite geometric series given #5/3-10/9+20/27-...#?
- How do you find the sum of the infinite geometric series given #3/2-3/4+3/8-...#?
- How do you find the sum of the infinite geometric series given #3+1.8+1.08+...#?
- How do you find the sum of the infinite geometric series given #1-0.5+0.25-...#?
- How do you find the sum of the infinite geometric series given #Sigma 48(2/3)^(n-1)# from n=1 to #oo#?
- How do you find the sum of the infinite geometric series given #Sigma (3/8)(3/4)^(n-1)# from n=1 to #oo#?
- How do you find the sum of the infinite geometric series given #Sigma3(0.5)^(n-1)# from n=1 to #oo#?
- How do you find the sum of the infinite geometric series given #Sigma(1.5)(0.25)^(n-1)# from n=1 to #oo#?
- A hot air balloon rises 90 feet in its first minute of flight. In each succeeding minute, it rises only 90% as far as it did during the preceding minute. What is the final height of the balloon?
- The sum of an infinite geometric series is 81, and its common ratio is 2/3, how do you find the first three terms of the series?
- The sum of an infinite geometric series is 125, and the value of r is 0.4. How do you find the first three terms of the series?
- The common ratio of an infinite geometric series is 11/16, and its sum is 76 4/5, how do you find the first four terms of the series?
- The first term of an infinite geometric series is -8, and its sum is -13 1/3, how do you find the first four terms of the series?
- How do you find the repeating decimal 0.7 with 7 repeated as a fraction?
- How do you find the repeating decimal 0.1 with 1 repeated as a fraction?
- How do you find the repeating decimal 0.36 with 36 repeated as a fraction?
- How do you find the repeating decimal 0.82 with 82 repeated as a fraction?
- How do you find the repeating decimal 0.427 with 427 repeated as a fraction?
- How do you find the repeating decimal 0.45 with 45 repeated as a fraction?
- How do you find the repeating decimal 0.231 with 31 repeated as a fraction?
- What is the sum of an infinite geometric series with a first term of 6 and a common ratio of 1/2?
- What is the sum of #7+77+777+7777+...# to #n# terms ?
- If the sum of the first three terms of a geometric sequence is #52#, and the common ratio is #3#, what are the first and sixth terms?
- Using mathematical induction for integers n #>=# 1, prove a + (a+d) +...+ (a+nd) = 1/2 (n+1)(2a+nd)?
- Find the sum of the series #1/2-1/3+1/4-1/9+1/8-1/27+........# to infinity?
- Question #75fee
- How do you prove that sum of infinite series #1+1/4+1/9+...............# is less than two?
- Question #34f1c
- If #sum c_nx_n# has a radius of convergence of #10# and #sum d_nx_n # has a radius of convergence of #11#, then what is radius of convergence of #sum (c_n + d_n)x_n#?
- What is the sum of #2/3+8/9+26/27+...# to #n# terms ?
- Question #2e7bb
- Does the following infinite series converge or diverge? 3/2 + 12/2 +48/2 +192/2
- What is the sum of the sequence #2, 5, 10, 17,...# up to #n# ?
- Does #a_n = (n+1)^(1/3)-n^(1/3)# converge?
- What is the sum #1+1/3+1/5+1/7+1/9+1/11+...# ?
- Find the infinite sum, if it exists: #–2+1/2-1/8+1/32-...#?
- Why is #1+2+3+... = -1/12# ?