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Prove the Following by Using the Principle of Mathematical Induction for All N ∈ N: 1^3 + 2^3 + 3^3 + ... + N^3 = ((N(N+1))/2)^2

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प्रश्न

Prove the following by using the principle of mathematical induction for all n ∈ N

`1^3 +  2^3 + 3^3 + ... + n^3 = ((n(n+1))/2)^2`

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उत्तर

Thus, P(k + 1) is true whenever P(k) is true.

Hence, by the principle of mathematical induction, statement P(n) is true for all natural numbers i.e., n.

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