Q13 of 27 Page 4

Prove the following by the principle of mathematical induction:

Let P(n):

For n= 1 is true,

P(1):

Since, P(n) is true for n = 1

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

- - - - (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:

Prove the following using the principle of mathematical induction for all n ∈ N

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

Prove the following by the principle of mathematical induction:

Prove the following using the principle of mathematical induction for all n ∈ N

a + ar + ar² + …+ ar^n–1 =

Questions · 27

4. Principle of Mathematical Induction

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