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.