Evaluate the series

Question

∑[i=0,∞,(1)/(4^(i))]

or

infinity

Sigma 1/4^i

i = 0

Thank you for any assistance

Answer 1

This is the series S=1/4⁰+1/4¹+1/4²+1/4³+... , which is a geometric progression.

S/4=1/4¹+1/4²+1/4³+...

S-S/4=¾S=1. 1/4ⁱ→0 as i→∞, so S=4/3 or 1⅓.