Let for n=1,2, . . . . . ., 50, S_n be the sum of the infinite geometric progression whose first term is n^2 and whose common ratio is \frac{1}{(n+1)^2}. Then the value of \frac{1}{26}+\sum_{n=1}^{50}(S_n+\frac{2}{n+1}-n-1) is equal to____ [28-Jun-2022-Shift-2]

JEE Main 28 June 2022 Shift 2 Solved Paper

Section: Mathematics

Question : 25 of 90

Marks: +1, -0

Let for n=1,2,......,50,Sn be the sum of the infinite geometric progression whose first term is n2 and whose common ratio is ‌

(n+1)2

. Then the value of
‌

∑

n=1

(Sn+‌

n+1

−n−1) is equal to____

[28-Jun-2022-Shift-2]

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