MathCastle
ChallengeMediumTelescoping & Recursion

Telescoping & Recursion · Medium problem

Compute ∑n=1991 nn+1+(n+1)n \displaystyle \sum_{n=1}^{99}\frac{1}{\,n\sqrt{n+1}+(n+1)\sqrt{n}\,}.

Express your answer as a common fraction.