Find the sum of series 13 + 33 + 53 +…………………………..+ 113. - Vidyadip

MCQ

Find the sum of series 1³+ 3³+ 5³+…………………………..+ 11³.

A
2556
B
5248
C
6589
D
9874

✓

Answer

2556

Solution:

1³+ 3³+ 5³+…………………………..+ 11³

= (1³+ 2³+ 3³+……+ 11³) – (2³+ 4³+ 6³+ 8³+ 10³)

= (1³+ 2³+ 3³+……11³) – 2³(1³+ 23 + 3³+ 4³+ 5³)

$\Big(\frac{11\times12}{2}\Big)^2-8\Big(\frac{5\times6}{2}\Big)^2$

$=66^2-8\times15^2$

$4356-1800=2556.$

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