Find the sum of series 1^2+3^2+5^2+ ………….+ 11^2. - Vidyadip

MCQ

Find the sum of series $ 1^2+3^2+5^2+\ldots………….+ 11^2$.

A
$279$
✓
$286$
C
$309$
D
$409$

✓

Answer

Correct option: B.

$286$

$1^2+3^2+5^2+\ldots…………..+ 11^2$
$=\left(1^2+2^2+3^2+\ldots \ldots+11^2\right)-\left(2^2+4^2+6^2+8^2+10^2\right) $
$=\left(1^2+2^2+3^2+\ldots . .11^2\right)-2^2\left(1^2+2^2+3^2+4^2+5^2\right)$
$=\frac{16\times12\times23}{6}-\frac{4\times5\times6\times11}{6}$
$=506-220$
$=286.$

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