Find the value of $1^{2} + 2^{2} + 3^{2} + . . . . . . . 30 t e r m s$ .

9455

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950

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465

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1055

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Solution

The correct option is A 9455
Given series is $1^{2} + 2^{2} + 3^{2} + . . . . . . . 30 t e r m s$ .
$∵$ Sum of squares of first 'n' natural numbers is $\frac{n \times (n + 1) \times (2 n + 1)}{6}$
Here, n = 30
$∴ 1^{2} + 2^{2} + 3^{2} + . . . . . . . 30 t e r m s = \frac{30 \times (30 + 1) \times (60 + 1)}{6}$
= $5 \times (31) \times (61)$
= 9455

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