A sequence x 1 , x 2 , x 3 , …. is defined by letting x 1 = 2 and for all natural numbers k, k ≥ 2. Show that for all n ϵ N

Question

Philoid · Accepted Answer

Step1: For n=1

So, it is true for n=1.

Step2: For n=k,

Now, we need to show P(k+1) is true whenever P(k) is true.

P(k+1):

So, it is true for n=k+1.

Thus, by the principle of mathematical induction P(n) is true.

A sequence x1, x2, x3, …. is defined by letting x1 = 2 and for all natural numbers k, k ≥ 2. Show that for all nϵN