The correct option is B n(n+1)(n+2)/3 S=Σ n^2 + Σ n Therefore, S=n(n+1)(2n+1)6+n(n+1)2 Hence, S=n(n+1)(n+2)3 ...

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Summation by Sigma Method

12+1+22+2+32+...

Question

$1^{2} + 1 + 2^{2} + 2 + 3^{2} + 3 + \dots . . + n^{2} + n =$

\frac{(n + 1) (n + 2)}{3}

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\frac{n (n + 1) (n + 2)}{3}

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\frac{n (n + 2) (n + 3)}{6}

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\frac{(n + 1) (n + 2) (n + 3)}{4}

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Solution

The correct option is B $\frac{n (n + 1) (n + 2)}{3}$
$S = Σ n^{2} + Σ n$
Therefore,
$S = \frac{n (n + 1) (2 n + 1)}{6} + \frac{n (n + 1)}{2}$
Hence,
$S = \frac{n (n + 1) (n + 2)}{3}$

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