Prove the following by the principle of mathematical induction:
Let P(n):
For n= 1is true
P(1): =
Since, P(n) is true for n =1
Let P(n) is true for n= k
P(n): - - - - - - - (1)
We have to show that,
Now,
=
=
=
=
=
=
=
Therefore, P(n) is true for n = k + 1
Hence, P(n) is true for all n∈ N