Prove that for all naturalnumbers, n ≥ 2.

Question

Prove that   for all naturalnumbers, n ≥ 2.

Philoid · Accepted Answer

Let P(n) =

Let us find if it is true at n = 2,

P(2):

Hence, P(2) holds.

Now let P(k) is true, and we have to prove that P(k + 1) is true.

Therefore, we need to prove that,

P(k) = …….(1)

Taking L.H.S of P(k) we get,

P(k) =

P(k + 1) =

From equation (1),

P(k + 1) =

Therefore, P(k + 1) holds.

Hence, P(n) is true for all n ≥ 2.

Prove that for all natural
numbers, n ≥ 2.