What is the total number of hours the battery can be used over its lifetime?

Question

After each charging, a battery is able to hold only 95% of the charge from the previous charging. The battery was used for 15 hours on its first charge before it had to be recharged. 

Answer 1

The first time the battery is used, it lasts 15 hours. The next time will be 15×0.95 hours. The third time, it will be 15×0.95² and so on. Adding up all of the hours between charges is a geometric series.

∞

S = ∑15(0.95)^i-1 = 15/(1-0.95) = 15/0.05 = 300 hours

i=1