What kind of series is $\sum_{n=0}^{\infty}{n\over{2^n}}$ ? - MathOverflow [closed]most recent 30 from http://mathoverflow.net2013-05-19T02:18:11Zhttp://mathoverflow.net/feeds/question/38937http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/38937/what-kind-of-series-is-sum-n0-inftyn-over2nWhat kind of series is $\sum_{n=0}^{\infty}{n\over{2^n}}$ ?foolip2010-09-16T07:02:56Z2010-09-16T07:02:56Z
<p>$\sum_{n=0}^{\infty}{n\over{2^n}}$</p>
<p>This series appears to converge to 2, but what kind of series is it?</p>
<p>(Source: "using mathematical formulas" in <a href="http://www.mytechinterviews.com/boys-and-girls" rel="nofollow">http://www.mytechinterviews.com/boys-and-girls</a>)</p>