Question

The sum of the series $1+2(1+1/n)+3(1+1/n{)}^2+....\infty$ is given by?

• A. $n^2+1$
• B. $n(n+1)$
• C. $n(1+1/n{)}^2$
• D. $n^2$

Answer 1

The correct option is D $n^2$

$S=1+2(1+\frac{1}{n})+3(1+\frac{1}{n}{)}^2+.....\infty$

$S(1+\frac{1}{n})=(1+\frac{1}{n})+2(1+\frac{1}{n}{)}^2+.......\infty$

$-\frac{S}{n}=1+(1+\frac{1}{n})+(1+\frac{1}{n}{)}^2+......\infty$

$-\frac{S}{n}=\frac{1}{1-(1+\frac{1}{n})}$

$S=n^2$