# Find $\lim\limits_{n\to\infty}\sum\limits_{k=1}^{n}\frac{2k-1}{2^k}$ [duplicate]

What is the method finding the closed form of $\displaystyle\sum_{k=1}^{n}\frac{2k-1}{2^k}$?

• You can use summation by parts. – Arbuja Jan 30 '16 at 17:35
• Don't look for "the" method; look for "a" method. You'll probably never find a math problem for which there is only one method of solving it. $\qquad$ – Michael Hardy Jan 30 '16 at 18:25