Infinite Sequences

Key Questions

• What is the difference between an infinite sequence and an infinite series?

  An infinite sequence of numbers is an ordered list of numbers with an infinite number of numbers.

  An infinite series can be thought of as the sum of an infinite sequence.

  Ahmed E. · 3 · Aug 21 2014
• How do you Determine whether an infinite sequence converges or diverges?

  The sequence `{a_n}` converges if `lim_{n to infty}a_n` exists (having a finite value); otherwise, it diverges.

  ---

  I hope that this was helpful.

  Wataru · · Oct 17 2014
• What is the definition of an infinite sequence?

  Informally, and (real-valued) infinite sequence is just an infinite list of real numbers `x_{1},x_{2},x_{3},x_{4},\ldots`.

  More precisely, an infinite sequence is a function whose domain can be taken (among other things) to be the set of positive integers `NN={\1,2,3,4,\ldots}` and whose codomain is the set of real numbers `RR`. The output of the sequence at the input `n\in NN` is `x_{n}\in RR`.

  Bill K. · 1 · May 20 2015

• What is the difference between an infinite sequence and an infinite series?
• What is the definition of an infinite sequence?
• How do you Find the limit of an infinite sequence?
• How do you Find the `n`-th term of the infinite sequence `1,1/4,1/9,1/16,…`?
• How do you Determine whether an infinite sequence converges or diverges?
• How do you determine whether the infinite sequence `a_n=(2n)/(n+1)` converges or diverges?
• How do you determine whether the infinite sequence `a_n=(1+1/n)^n` converges or diverges?
• How do you determine whether the infinite sequence `a_n=(-1)^n` converges or diverges?
• How do you Find the `n`-th term of the infinite sequence `1,-2/3,4/9,-8/27,…`?
• How do you determine whether the infinite sequence `a_n=e^(1/n)` converges or diverges?
• How do you determine whether the infinite sequence `a_n=arctan(2n)` converges or diverges?
• How do you determine whether the infinite sequence `a_n=n*cos(n*pi)` converges or diverges?
• How do you determine whether the infinite sequence `a_n=n+1/n` converges or diverges?
• How do I find a formula for `s_n` for the sequence -2, 1, 6, 13, 22,...?
• How do you find a formula for the sequence -2, 1, 6, 13, 22..?
• What does it mean for a sequence to converge?
• Does `a_n={(3/n)^(1/n)}`converge? If so what is the limit?
• Does `a_n=n*{(3/n)^(1/n)}`converge? If so what is the limit?
• Does `a_n=(5^n)/(1+(6^n)`converge? If so what is the limit?
• Does `a_n=(2+n+(n^3))/sqrt(2+(n^2)+(n^8))`converge? If so what is the limit?
• Does `a_n=(8000n)/(.0001n^2)`converge? If so what is the limit?
• If `a_n` converges and `a_n >b_n` for all n, does `b_n` converge?
• If `a_n` converges and `lim_(n->oo) a_n -b_n=c`, where c is a constant, does `b_n` converge?
• If `a_n` converges and `lim_(n->oo) a_n /b_n=0`, where c is a constant, does `b_n` necessarily converge?
• Does `a_n=(1 + (n/2))^n` converge?
• Does `a_n=(n + (n/2))^(1/n)` converge?
• What is the root test?
• Does `a_n=1/(n!)` converge?
• Does `a_n=n^n/(n!)` converge?
• Does `a_n=n^x/(n!)` converge for any x?
• Does `a_n=x^n/(n!)` converge for any x?
• Does `a_n=x^n/(xn!)` converge for any x?
• Does `a_n=1/(n^2+1)` converge?
• Does `a_n=lnn/(n^2+1)` converge?
• Does `a_n=2^n/(n^2+1)` converge?
• Does `a_n=x^n/n^x` converge for any x?
• Suppose, `a_n` is monotone and converges and `b_n=(a_n)^2`. Does `b_n` necessarily converge?
• What does it mean for a sequence to be monotone?
• What is an alternating sequence?
• Does `a_n=sin(n)/n` converge?
• Question #c0aff
• How do you find the nth term of the sequence `1/2, 1/4, 1/8, 1/16, ...`?
• How do you find the nth term of the sequence `1/2, 2/3, 3/4, 4/5, ...`?
• How do you find the nth term of the sequence `2,5,10,17,26,37,...`?
• How do you find the nth term of the sequence `1, 1 1/2, 1 3/4, 1 7/8, ...`?
• How do you find the nth term of the sequence `1, 3, 6, 10, 15,...`?
• How do you find the nth term of the sequence `2, 4, 16, 256, ...`?
• How do you find the nth term of the sequence `0.6, 0.61, 0.616, 0.6161,...`?
• How do you determine whether the sequence `a_n=sqrtn` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=(n+2)/n` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=n-n^2/(n+1)` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=n(-1)^n` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=(-1)^n/sqrtn` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=n/(ln(n)^2` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=rootn (n)` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=ln(ln(n))` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=sqrt(n^2+n)-n` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=((n-1)/n)^n` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=(n^3-2)/(n^2+5)` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=(2^n+3^n)/(2^n-3^n)` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=2^n-n^2` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=n!-10^n` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=(n!+2)/((n+1)!+1)` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=(n!)^(1/n)` converges, if so how do you find the limit?
• How do you determine whether the sequence `a_n=(n+1)^n/n^(n+1)` converges, if so how do you find the limit?
• How do you determine if `a_n=1+3/7+9/49+...+(3/7)^n+...` converge and find the sums when they exist?
• How do you determine if `a_n=1-1.1+1.11-1.111+1.1111-...` converge and find the sums when they exist?
• How do you determine if `a_n=(1-1/8)+(1/8-1/27)+(1/27-1/64)+...+(1/n^3-1/(n+1)^3)+...` converge and find the sums when they exist?
• How do you determine if `a_n=6+19+3+4/25+8/125+16/625+...+(2/5)^n+...` converge and find the sums when they exist?
• How do you determine if `Sigma (7^n-6^n)/5^n` from `n=[0,oo)` converge and find the sums when they exist?
• How do you determine if `Sigma (7*5^n)/6^n` from `n=[0,oo)` converge and find the sums when they exist?
• How do you determine if `Sigma (2n-3)/(5n+6)` from `n=[0,oo)` converge and find the sums when they exist?
• Sequence ?
• Converge sequence !!!?
• `X_(n+1)-aX_n+2=0` Which are the set values of "a" for the string "Xn" is descending?
• Question #351d2
• Question #8d080
• We have `f(n)` an string;`ninNN` such that `f(n+1)-f(n)=3f(n)` and `f(0)=-1/2`.How to express `f(n)` according to `n`?
• Is the sequence `a_n=(1+3/n)^(4n)` convergent or divergent?
• Check for convergence or divergence in the following sequences?