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

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Solution

The correct option is A

$T_{π}$ = $n^{2}$ + n ⇒ $S_{π}$ = $\sum T_{π}$ = $\sum$ $n^{2}$ + $\sum$ n

= $\frac{n (n + 1) (2 n + 1)}{6}$ + $\frac{n (n + 1)}{2}$

= $\frac{n (n + 1)}{6}$ {2n + 1 + 3} = $\frac{n (n + 1) (n + 2)}{3}$

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