# Geometric-type series

• October 12th 2009, 11:04 AM
SlipStream
Geometric-type series
Is there a closed-form expression for series of the type

$
\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!