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 .