Question

How do you find the nth partial sum, determine whether the series converges and find the sum when it exists given `1-1/3+1/9-...+(-1/3)^n+...`?

Answer 1

`0.75`

Explanation:

The Maclaurin series

`1/(1+x)=1-x+x^2-x^3+...` is valid for `-1 < x <1`.

Here, x = 1/3.

So, the given series converges to `1/(1+1/3)=0.75`.