For positive integers

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

For positive integers

k=1,2,3,\ldots,n

, let

S_k

denote the area of

\triangle OAB_k

, where

O

is the origin,

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

,

OA=1

, and

OB_k=k

. The value of

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

is (1)

\frac{2}{\pi^2}

(2)

\frac{4}{\pi^2}

(3)

\frac{8}{\pi^2}

(4)

\frac{1}{2\pi^2}

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