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Given sum can be written as lim n!1 Xn k=1 1 n ( k n ) sec2 k2 n2 wR hich is limit of Riemann sum of f(x) = x sec2 x over the interval [0,1]. Thus the limit of required sum is 1 0 [x sec2(x2)]dx = (tan 1)=2.

Given sum can be written as
lim
n!1
Xn
k=1
1
n
(
k
n
) sec2 k2
n2
wR hich is limit of Riemann sum of f(x) = x sec2 x over the interval [0,1]. Thus the limit of required sum is 1
0 [x sec2(x2)]dx = (tan 1)=2.

Grade:12

1 Answers

Girish Kadam
askIITians Faculty 14 Points
10 years ago
Dear Student, There is a error in the format. Please post the question again. askIITian Faculty

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