(when ) is equal to

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

\lim_{n \rightarrow \infty}\left\{\left(\frac{n}{n+1}\right)^a + \sin\frac{1}{n}\right\}^n

(when

a \in \mathbb{Q}

) is equal to (a)

e^{-a}

(b)

-a

(c)

e^{1-a}

(d)

e^{1+a}