Hi, a naive question here, but I was wondering if the series(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\sum^{∞}_{k=0}[/itex] k a[itex]^{k}[/itex]

has a particular name? As in 'geometric series' for [itex]\sum^{∞}_{k=0}[/itex] a[itex]^{k}[/itex] ?

And what about the more general [itex]\sum^{∞}_{k=0}[/itex] k[itex]^{n}[/itex] a[itex]^{k}[/itex] ?

As a related question, you seem to be able to get the formula for the sum by differentiating the formula for the geometric series. Is this a correct and mathematically rigorous way to do it?

Cheers,

zeroseven

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# Does the series k a^k have a name?

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