Question

The sum of $n$ terms of the series whose $n^{th}$ term is $n(n+1)$ is equal to.

• A. $\frac{n(n+1)(n+2)}{3}$
• B. $\frac{(n+1)(n+2)(n+3)}{12}$
• C. $n^2(n+2)$
• D. $n(n+1)(n+2)$

Answer 1

The correct option is A $\frac{n(n+1)(n+2)}{3}$

$T_n=n(n+1)=n^2+n$
$\therefore$ Sum $=$ $S_n=\sum T_n=\sum n^2+\sum n=\frac{n(n+1)(2n+1)}{6}+\frac{n(n+1)}{2}$
$=\frac{n(n+1)}{6}(2n+1+3)=\frac{n(n+1)(n+2)}{3}$
Hence, option 'A' is correct.