If upto terms then the sum of the infinite terms is :

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

Problem

S_n = \frac{1 \cdot 2}{3!} + \frac{2 \cdot 2^2}{4!} + \frac{3 \cdot 2^3}{5!} + \dots

upto

n

terms then the sum of the infinite terms is : (a) 1 (b)

\frac{2}{3}

(c)

e

(d)

\frac{\pi}{4}