Question

Find the value of
1^3+3^3+5^3+7^3+9^3+11^3+..............+29^3=? With formula?

Answer 1

we can write above question as

$( {1}^{3} + {2}^{3} + .... + {29}^{3} ) - ( {2}^{3} + {4}^{3} + .... {28}^{3} ) \\ = ( {1}^{3} + ....+ {29}^{3} ) - {2}^{3} ( {1}^{3} + .... + {14}^{3} ) \\ = { (\frac{29.(29+ 1)}{2} )}^{2} - 8 {( \frac{14.(14 + 1)}{2} )}^{2} \\ = 189225 - 88200 \\ = 101025$

Answer 2

Answer:

we can write above question as

(1³ +2³+ +29³)- (2³ +4³ +....28³)

(1³+ +29³) - 2³ (1³ + +14³)

189225-88200

=101025