NCERT Class 11-Math's: Chapter –4 Principle of Mathematical Induction Part 8

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Question 21:

Prove that, , for all .

Answer:

Let .

Step1:

Step2: Assume is true for some ………………… (i) is true.

Step3: Now we have to prove

Multiplying both sides of equation (i) by

is true

Hence, is true whenever is true

Therefore by the principle of mathematical induction we have is true for all .

Question 22:

Prove that, , for all .

Answer:

It’s true at .

Let

Be true

By mathematical Induction is true for all natural number n.