# NCERT Class 11-Math's: Chapter –4 Principle of Mathematical Induction Part 6

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**Question 16:**

for all natural numbers .

**Answer:**

is true;

## Long Answer Type

### Use the Principle of Mathematical Induction in the Following Exercises

**Question 17:**

A sequence ... is defined by letting and for all natural numbers . Show that for all natural numbers.

**Answer:**

Given;

Let be true.

is true when is true.

∴ By Mathematical Induction is true for all natural numbers n.

**Question 18:**

A sequence ... is defined by letting and for all natural numbers . Show that for all natural number *n* using mathematical induction.

**Answer:**

Given; A sequence … is defined by letting for all natural numbers .

Let be true.

is true when is true.

By mathematical Induction is true for all natural numbers .

**Question 19:**

A sequence is defined by letting and for all natural numbers, Show that For all .

**Answer:**

Given; A sequence … Is defined by letting

Let Be true.

is true when is true.

By Mathematical Induction Is true for all natural numbers .