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

Doorsteptutor material for UGC Public-Administration is prepared by world's top subject experts: fully solved questions with step-by-step explanation- practice your way to success.

Question 21:

Prove that, , for all .

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 .