Question

Given a series 1 + 1/2 + 1/4 + 1/8 + 1/16+......; determine the nature of the series, the sum of the n term of the series and sim of the terms as n tends to infinity.

Answer 1

It's an inverse power series,

$S_n=2\cdot(1-(\frac{1}{2})^n),\\S=2.$