Matematické Fórum

stuart clark · 29. 12. 2011 08:51

find sum of $\frac{1}{1+x}+\frac{2x}{1+x^2}+\frac{3x^2}{1+x^3}+.............\infty$

vanok · 08. 01. 2012 16:53

Hi ↑ stuart clark:,

Let us the sum of the series by $S$ .

I give here formal solution, without worrying about the convergence
We observe that the general term of the series can spell
$\frac{kx^{k-1}}{1+x^k}=\frac{(1+x^k)'}{1+x^k}$
An indefinite integral of which is
$\ln|1+x^k|$
So we have formally
$S=$ \lim_{n\to +\infty}{\prod_{1}^{n}}\ln|1+x^k| $'$

By completing the problems connected in convergence, the solution will be complete.

stuart clark · 10. 01. 2012 09:25

Thanks vanok but after that how can i solve it

Matematické Fórum

#1 29. 12. 2011 08:51

infinite series sum

#2 08. 01. 2012 16:53

Re: infinite series sum

#3 10. 01. 2012 09:25

Re: infinite series sum

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