Sum of the series $1^{2} .2 + 2^{2} .3 + 3^{2} .4 +$ ........................upto 10 terms is.

2400

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3410

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1800

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2490

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Solution

The correct option is D $3410$
99804 : (B)
$a_{n} = n^{2} (n + 1)$ $1 \leq n \leq 10$

$S =^{10} \sum_{a n} = \sum_{n} n^{2} (n + 1) = \sum_{n} n^{3} + \sum_{n} n^{2}$

$= ∣ ∣ ∣ ∣ {[n \frac{(n + 1)}{2}]}^{2} + n \frac{(n + 1) (2 n + 1)}{6} ∣ ∣ ∣ ∣$
$2_{10}$
$= 55^{2} + 385 = 3410$

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