Let be a positive real number

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

Problem

Let

k

be a positive real number. Determine the value of

\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}\frac{k}{n}\,\sin\!\Bigl(\frac{k\,i}{n}\Bigr)

in terms of

k

. (a)

\dfrac{1-\cos k}{k}

(b)

k\sin k

(c)

1-\cos k

(d)

k(1-\cos k)