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

MCQ

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

✓
$2556$
B
$5248$
C
$6589$
D
$9874$

✓

Answer

Correct option: A.

$2556$

$1^3+ 3^3+ 5^3+……………..+ 11^3$
$= (1^3+ 2^3+ 3^3+……+ 11^3) – (2^3+ 4^3+ 6^3+ 8^3+ 10^3)$
$= (1^3+ 2^3+ 3^3+……11^3) – 2^3(1^3+ 23 + 3^3+ 4^3+ 5^3)$
$\Big(\frac{11\times12}{2}\Big)^2-8\Big(\frac{5\times6}{2}\Big)^2$
$=66^2-8\times15^2$
$4356-1800=2556.$

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