Question

For all n ∈ N, by using principle of mathematical induction, then prove that:

1³ + 2³ + 3³ + ... + n³ = [(n(n + 1))/2]²

Answer 1

Let the given statement is P(n) when n ∈ N

i.e., P(n) = 1³ + 2³ + 3³ + ……. + n³ = [(n( + 1))/2]²

Now, we have to prove that given statement is true for n

Here, given statement is also true for n = m + 1,

i.e., P(m + 1) is also true.

Hence, by the principle of mathematical induction,

we can say that the given statement is true for each natural number n ∈ N.

Hence Proved