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Question: Does this series converge?

Question:Does this series converge?

Scimann 511
infinity sum assuming symbolic series
May 31 2011
2

Why does this happen to Maple 15?

    `assuming`([sum(k*p*Beta(k, p+1), k = 1 .. infinity)], [p > 1]); eval(%, p = 2)

Is it possible to show with Maple that for any real p>1 the series converges to p/(p-1), e.g.,

    `assuming`([sum(k*p*Beta(k, p+1), k = 1 .. 1000)], [p > 1]): subs(p = 2, %): evalf(%)

How do I show this symbolically? Thanks.
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