1. ## geometric series

A geometric series has first term 10 and common ratio 0.02

a) find the sum to infinity

b) how many terms are needed so that their sum differs from the sum to infinity by less than 0.000 01?

2. The sum of an infinite geometric series is $\frac{a}{1 - r}$, where a is the first term and r is the common ratio. The sum of the first n terms is $\frac{a(1 - r^n)}{1 - r}$.