# 009C Sample Midterm 1, Problem 2

Consider the infinite series  ${\displaystyle \sum _{n=2}^{\infty }2{\bigg (}{\frac {1}{2^{n}}}-{\frac {1}{2^{n+1}}}{\bigg )}.}$
(a) Find an expression for the  ${\displaystyle n}$th partial sum  ${\displaystyle s_{n}}$  of the series.
(b) Compute  ${\displaystyle \lim _{n\rightarrow \infty }s_{n}.}$