Question

Which of the following series are geometric series? Find the sum if they are

1.
Infinity (Summation sign) n = 1
1/6n^2

2.
Infinity (Summation sign) n = 1
(0.6)^n-1

Answer 1

1. Apparently you mean the sum from n=1 to n=infinity of 1/(6n^2)

= 1/(6*1) + 1/(6*4) + 1/6*9)
= (1/6)(1 + 1/4 + 1/9 + 1/16 + ...)]
This is not a geometric series. The ratio of successive terms is not a constant.

2. 0.6 + 0.6^2 + 0.6^3 + ...
= 0.6(1 + 0.6 + 0.6^2 + ...]
= 0.6/[1 - 0.6)= 1.5
This is a geometric series.