Mathematica and infinite series

*To*: mathgroup at smc.vnet.net*Subject*: [mg113185] Mathematica and infinite series*From*: Sam Takoy <sam.takoy at yahoo.com>*Date*: Sun, 17 Oct 2010 06:06:03 -0400 (EDT)

Hi, I am about to embark on a project that operates heavily in infinite series, so I started figuring out Mathematica's basis capabilities. I found them very impressive, but I came across this: f[x_] := Sum[Log[n]/(n^2 Factorial[n]) x^n, {n, 1, Infinity}] Assuming[n > 0, SeriesCoefficient[f[x], {x, 0, 4}]] Answer: SeriesCoefficient[\!\( \*UnderoverscriptBox[\(\[Sum]\), \(n = 1\), \(\[Infinity]\)] \*FractionBox[\( \*SuperscriptBox[\(x\), \(n\)]\ Log[n]\), \( \*SuperscriptBox[\(n\), \(2\)]\ \(n!\)\)]\), {x, 0, 4}] Why doesn't Mathematica produce Log[n]/(n^2 Factorial[n]) as the answer? Thanks! Sam