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Black Advanced Problems in Mathematics

Exam: Black Advanced Problems in Mathematics
Subject: Mathematics
Chapter: Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

For positive integers k = 1, 2, 3 , n , let S_k denotes the area of...

For positive integers

k = 1, 2, 3 \dots , n

, let

S_k

denotes the area of

\Delta AOB_k

(where 'O' is origin) such that

\angle AOB_k = \frac{k\pi}{2n}

,

OA = 1

and

OB_k = k

. The value of the

\lim_{n \to \infty} \frac{1}{n^2} \sum_{k=1}^n S_k

is :

Options

A $\frac{2}{\pi^2}$
B $\frac{4}{\pi^2}$
C $\frac{8}{\pi^2}$
D $\frac{1}{2\pi^2}$

Correct answer

D. $\frac{1}{2\pi^2}$

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