Question

How do you find what this series converges to? -1/7 Σ (n=0 to infinity) ((4^n)/(-5)^(2n-2))

Answer 1

`-625/147`

Explanation:

`-1/7 ×sum_(n=0) ^oo ((4^n)/(-5)^(2n-2))`

`= -1/7×(25 + 4 + 16/25 + 64/125 + ...)`

`= -1/7×(25/(1 - 4/25))`

`= -1/7×(25/(1 - 4/25))`

`= -625/147`