Check sibling questions

Example 3 - Chapter 4 Class 11 Mathematical Induction

Last updated at Dec. 8, 2016 by

Example 3 - Prove 1/1.2 + 1/2.3 + 1/3.4 .. + 1/n(n + 1) = 1/n+1 - Equal - 1 upon addition

Example 3 - Chapter 4 Class 11 Mathematical Induction - Part 2
Example 3 - Chapter 4 Class 11 Mathematical Induction - Part 3
Example 3 - Chapter 4 Class 11 Mathematical Induction - Part 4

This video is only available for Teachoo black users

Subscribe Now

Solve all your doubts with Teachoo Black (new monthly pack available now!)

Join Teachoo Black

Transcript

Example 3 For all n β‰₯ 1, prove that 1/1.2 + 1/2.3 + 1/3.4 +…….+ 1/(𝑛(𝑛 + 1)) = 1/(𝑛 + 1) Let P (n) : 1/1.2 + 1/2.3 + 1/3.4 +…….+ 1/(𝑛(𝑛 + 1)) = 1/(𝑛 + 1) For n=1, L.H.S = 1/1.2 = 1/2 R.H.S = 1/(1+1) = 1/2 Hence, L.H.S. = R.H.S , ∴ P(n) is true for n = 1 Assume P(k) is true 1/1.2 + 1/2.3 + 1/3.4 +…….+ 1/(π‘˜(π‘˜+1)) = π‘˜/(π‘˜+1) We will prove that P(k + 1) is true. R.H.S = ((k + 1))/(((k + 1)+ 1) ) L.H.S =1/1.2 + 1/2.3 + 1/3.4 +…….+ 1/((k + 1)((k + 1)+ 1)) ∴ By the principle of mathematical induction, P(n) is true for n, where n is a natural number

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.