3. Use the concept of a series to sum up 0.315+0.000315+0.000000315+ Give your final answer
in reduced fraction form. Note: There are several methods to prove this fact. I am specifically asking
you to use a series.

Dividing each term in the given series by 0.315 reveals a simple geometric sum,

0.315 (1 + 1/1,000 + 1/1,000,000 + …)

or

0.315 (1 + 1/10³ + 1/10⁶ + …)

or

i.e. a geometric sum with a common ratio of 1/1,000. I'm not sure what your instructor expects exactly, but you may already know that

if |r | < 1. This is the case here, so

0.315 (1 + 1/1,000 + 1/1,000,000 + …) = 0.315 / (1 - 1/1,000)

… = (315/1000) / (999/1000)

… = 315/999

… = 35/111

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3