Is there a closed-form expression for series of the type

$\displaystyle

\sum_{n=1}^\infty n^t \cdot r ^ {n - 1}

$

Where |r| < 1 and t is a positive integer?

Is there a name for this type of series? A special case of hypergeometric?

Thanks!

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- Oct 12th 2009, 11:04 AMSlipStreamGeometric-type series
Is there a closed-form expression for series of the type

$\displaystyle

\sum_{n=1}^\infty n^t \cdot r ^ {n - 1}

$

Where |r| < 1 and t is a positive integer?

Is there a name for this type of series? A special case of hypergeometric?

Thanks!