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Question

Find the sum of the cubes of first five natural numbers. Verify your answer by using formula (n)(n+1)/2]2, where n is a natural numbers. Also find the sum of the cubs of the first ten natural numbers.

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Solution

S=13+23+33+43............+n3
n4(n1)1=4n36n2+4n1
n4=4S6n(n+1)(2n+1)6+2n(n+1)n
4S=n4+n(n+1)(2n+1)2n(n+1)+n
4S=n4+n(2n2+3n+1)2n22n+n
4A=n4+2n3+3n2+n2n22n+n
4S=n4+2n3+n2
4S=n2(n2+2n+1)
4S=n2(n+1)2
S=[n(n+1)2]2

first ten terms
S=[10(11)2]2
S=55×55
=3025

5555___275275×______3025




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