Prove the following by the principle of mathematical induction:
Let P(n):
Step1: Let us verify P(1).
P(1):
P(1):
Therefore, P(1) is true.
Step 2:
Let P(k) is true.
Therefore, P(k):
Now we have to prove that P(k + 1) is also true.
So,
L.H.S =
L.H.S =
Now from P(k) we can say that,
Putting this value, we get,
L.H.S =
L.H.S =
L.H.S =
L.H.S = R.H.S
Hence, Proved.