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Question: The sum of \(1^{3} + 2^{3} + 3^{3} + 4^{3} + .... + 15^{3}\) is...

The sum of 13+23+33+43+....+1531^{3} + 2^{3} + 3^{3} + 4^{3} + .... + 15^{3} is

A

22000

B

10000

C

14400

D

15000

Answer

14400

Explanation

Solution

S=13+23+33+......+153S = 1^{3} + 2^{3} + 3^{3} + ...... + 15^{3} ; For n=15n = 15, the value of

(n(n+1)2)2=(15×162)2=14400\left( \frac{n(n + 1)}{2} \right)^{2} = \left( \frac{15 \times 16}{2} \right)^{2} = 14400