Question

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

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

Answer 1

Let the given statements is P(n), where n ∈ N,

Hence, given statement is true for n = 1, 

i.e, P(1) is true

Let the given statement is true for n = m, i.e,

Hence, the given statement is true for n = m + 1,

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