How do you find the sum of the infinite geometric series given #5/3-10/9+20/27-...#?
3 Answers
Explanation:
We first find the factor :
The sum of an infinite geometric series is given by the formula :
So the sum is :
Sum of the infinite geometric series is
Explanation:
In the series
whilr first term
As for common ratio
sum of the infinite geometric series is
Explanation:
#"for a geometric sequence the sum of n terms is"#
#S_n=(a(1-r^n))/(1-r);(r!=1)#
#"where a is the first term and r, the common ratio"#
#"as " ntooo,r^nto0" and " S_n" can be expressed as"#
#S_oo=a/(1-r);(|r|<1)#
#rArrr=(-10/9)/(5/3)=-2/3rarr|r|<1#
#rArrS_oo=(5/3)/(1+2/3)=1#