MathDB

2

Part of 2013 India PRMO

Problems(1)

2013 preRMO p2, S_n=\sum_{k=0}^{n}\frac{1}{\sqrt{k+1}+\sqrt{k}}

Source:

8/8/2019
Let Sn=∑k=0n1k+1+kS_n=\sum_{k=0}^{n}\frac{1}{\sqrt{k+1}+\sqrt{k}}. What is the value of ∑n=1991Sn+Sn−1\sum_{n=1}^{99}\frac{1}{S_n+S_{n-1}} ?
Sumalgebra