Using the princip

To Prove:

Steps to prove by mathematical induction:

Let P(n) be a statement involving the natural number n such that

(i) P(1) is true

(ii) P(k + 1) is true, whenever P(k) is true

Then P(n) is true for all n ϵ N

Therefore,

Let P(n):

Step 1:

P(1) =

Therefore, P(1) is true

Step 2:

Let P(k) is true Then,

P(k):

Now,

=

=

=

=

= P(k + 1)

Hence, P(k + 1) is true whenever P(k) is true

Hence, by the principle of mathematical induction, we have

for all n ϵ N