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Summation by Sigma Method

The sum of th...

Question

The sum of the series $1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . . . . . + 15^{2}$ is:

A

1080

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B

1240

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C

1460

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D

1620

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Solution

The correct option is B $1240$
The sum of the squares of the first n natural number is
$\frac{n (n + 1) (2 n + 1)}{6}$
Put $n = 15$ , we have,
$1^{2} + 2^{2} + 3^{2} + 4^{2} + . . . . . . . . . + 15^{2}$
$= \frac{15 (15 + 1) (30 + 1)}{6} = 1240$

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