prove by mathematical induction that 1^3 +2^3 + 3^3 +...+ n^3 = [ ( n (n+1) ) /2 ] ^2

prove by mathematical induction that 1^3 +2^3 + 3^3 +...+ n^3 = [ ( n (n+1) ) /2 ] ^2
(sum of the cubes of the first n natural numbers)

Also P(1) is true (proved earlier)

Hence by the principle of mathematical induction P(n) is true for all positve integers n = 1,2,3 , ...

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