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India Pre-Regional Mathematical Olympiad
2013 India PRMO
2
2013 preRMO p2, S_n=\sum_{k=0}^{n}\frac{1}{\sqrt{k+1}+\sqrt{k}}
2013 preRMO p2, S_n=\sum_{k=0}^{n}\frac{1}{\sqrt{k+1}+\sqrt{k}}
Source:
August 8, 2019
Sum
algebra
Problem Statement
Let
S
n
=
∑
k
=
0
n
1
k
+
1
+
k
S_n=\sum_{k=0}^{n}\frac{1}{\sqrt{k+1}+\sqrt{k}}
S
n
=
∑
k
=
0
n
k
+
1
+
k
1
. What is the value of
∑
n
=
1
99
1
S
n
+
S
n
−
1
\sum_{n=1}^{99}\frac{1}{S_n+S_{n-1}}
∑
n
=
1
99
S
n
+
S
n
−
1
1
?
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