series summation

From: Norman B. Grover <norman@xxxxxxxxxxxxx>
Date: Wed, 27 Jul 2005 09:00:49 +0300

Consider the following series: S(n)=1*1/2+2*2/4+3*3/8+4*4/16+5*5/32+...
+n*n/2^n. Does anyone know what S(n) evaluates to or whether S(infinity)
even exists? I couldn't find it in Jolley and don't know where else to
look.
Thank you.
--

Norman B. Grover
Jerusalem, Israel
.

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