Prove the following by the principle of mathematical induction:

Let P(n):

Step 1: Let us check if P(1) is true or not,

P(1):

Therefore, P(1) is true.

Step 2: Let us assume that P(k) is true, now we have to prove that P(k + 1) is true.

P(k):

P(k+1):

From P(k) we can see that,

P(k + 1):

P(k + 1):

P(k + 1):

Therefore, P(k + 1) is true.

Hence, Proved by mathematical induction.