Matematické Fórum

stuart clark · 29. 12. 2011 08:55

find sum of convergent series

$\frac{x^6}{6}-\frac{x^{16}}{16}+\frac{x^{26}}{26}+........................\infty$

vanok · 08. 01. 2012 18:01 — Editoval vanok (05. 03. 2012 00:54)

Hi ↑ stuart clark:,

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

I give here only an idea (doubtless false), because the derivation of the series does not work generally.
We observe that the general term of the series can spell
$(-1)^k\frac {x^{6+10k}}{6+10k}$
Of which the derivate is
$(-1)^k{x^{5+10k}}$ for $k=0; 1;..$
Let $y=x^5$
What gives
$(-1)^k{y^{1+2k}}$ for $k=0; 1;..$
Looked sum S is an indefinite integral of $\Sigma$ for a suitable constant C.

It remains to complete the problems connected to the convergence and to express $\Sigma$ and then $S$

Matematické Fórum

#1 29. 12. 2011 08:55

convergent series sum

#2 08. 01. 2012 18:01 — Editoval vanok (05. 03. 2012 00:54)

Re: convergent series sum

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