What kind of series is $\sum_{n=0}^{\infty}{n\over{2^n}}$ ? - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-19T02:18:11Z http://mathoverflow.net/feeds/question/38937 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/38937/what-kind-of-series-is-sum-n0-inftyn-over2n What kind of series is $\sum_{n=0}^{\infty}{n\over{2^n}}$ ? foolip 2010-09-16T07:02:56Z 2010-09-16T07:02:56Z <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>