The sum of the series upto terms is equal :

MATHEMATICS · Single correct · ISC · Mathematics · Algebra · Algebra

Problem

The sum of the series

\frac{2}{1 \cdot 2} + \frac{5}{2 \cdot 3} 2^1 + \frac{10}{3 \cdot 4} 2^2 + \frac{17}{4 \cdot 5} 2^3 + \dots

upto

n

terms is equal : (a)

\frac{n2^n}{n+1}

(b)

\left(\frac{n}{n+1}\right) 2^n + 1

(c)

\frac{n2^n}{n+1} - 1

(d)

\frac{(n-1)2^n}{n+1}