009C Sample Midterm 1, Problem 2

Consider the infinite series  $\sum _{n=2}^{\infty }2{\bigg (}{\frac {1}{2^{n}}}-{\frac {1}{2^{n+1}}}{\bigg )}.$

(a) Find an expression for the  $n$th partial sum  $s_{n}$  of the series.

(b) Compute  $\lim _{n\rightarrow \infty }s_{n}.$

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