Prove the following by using the principle of mathematical induction for all `n in N` : `1^3+2^3+3^3+""dot""""dot""""dot+n^3=((n(n+1))/2)^2`

Explanation

Given,

`1^3+2^3+3^3+""dot""""dot""""dot+n^3=((n(n+1))/2)^2`

For n=1`L.H.S=1^3=((1(1+1))/2)^2
=1`

`L.H.S=R.H.S`

so,P(1) is true

Let P(k)be true

`1^3+2^3+3^3+""dot""""dot""""dot+k^3=((k(k+1))/2)^2`

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