Q4 of 66 Page 12

Prove the following by the principle of mathematical induction:

Let P(n):

For n = 1

P(1):

= P(n) is true for n = 1

Let P(n) is true for n = k, So

- - - - - (1)

Now, Let P(n) is true for n = k + 1, So

Then,

Therefore, P(n) is true for n = k + 1

Hence, P(n) is true for all n∈N

Prove the following by the principle of mathematical induction:

To prove: Prove that by the Mathematical Induction.

Prove the following by the principle of mathematical induction:

i.e., the sum of first n odd natural numbers is n².

Prove the following by the principle of mathematical induction: