Is there a closed formula for the following sum involving binomials: $\sum_{s=t}^{t+d}\binom{s}{t}\frac{1}{s+1}$ where t,d>=0?

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- June 5th 2012, 02:33 AMobergurusum involving binomials
Is there a closed formula for the following sum involving binomials: $\sum_{s=t}^{t+d}\binom{s}{t}\frac{1}{s+1}$ where t,d>=0?

- June 5th 2012, 04:32 AMtom@ballooncalculusRe: sum involving binomials
- June 5th 2012, 06:33 AMoberguruRe: sum involving binomials
gr8 many thanks, tom. but i'm looking for a formula that does not involve sums or (unresolved) hypergeometric series :( moreover, the wolfram solution contains the value of the Gamma function for negative integers :(