Q9 of 66 Page 12

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

Prove the following by the principle of mathematical induction:

1.2 + 2.2² + 3.2³ + … + n.2ⁿ=(n–1) 2^{n + 1} + 2

Prove the following by the principle of mathematical induction:

2 + 5 + 8 + 11 + … + (3n – 1) = 1/2 n(3n + 1)