I'm not sure how to tackle this problem:
If the nth partial sum of a series a(n) from 1 to infinity is s(n)=3-n(2)^(-n), find a(n) and the sum of a(n) from n=1 to infinity.
Thanks
So $\displaystyle \sum_{k=1}^n a(k) = s(n) = 3-n2^{-n}$ right?
Well hint for part one: Note that $\displaystyle s(n)-s(n-1)=\sum_{k=1}^n a(k) - \sum_{k=1}^{n-1} a(k) = a(n)$
Hint for part two: $\displaystyle \sum_{k=1}^\infty a(k) = \lim_{n\rightarrow \infty} \sum_{k=1}^n a(k) = \lim_{n\rightarrow \infty} s(n)$