Mathematical Induction - Questions and Solutions

Examples →
Mathematical Induction
Serial order wise

Question 16 - Mathematical Induction - Questions and Solutions - Mathematical Induction

Last updated at May 29, 2023 by

Ex 4.1, 16 - Prove 1/1.4 + 1/4.7 ... + 1/(3n-2)(3n+1) = n/(3n+1) - Equal - 1 upon addition

Ex 4.1, 16 - Chapter 4 Class 11 Mathematical Induction - Part 2
Ex 4.1, 16 - Chapter 4 Class 11 Mathematical Induction - Part 3 Ex 4.1, 16 - Chapter 4 Class 11 Mathematical Induction - Part 4

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

Question16 Prove the following by using the principle of mathematical induction for all n ∈ N: 1/1.4 + 1/4.7 + 1/7.10 +…….+ 1/((3𝑛 − 2)(3𝑛 + 1)) = 𝑛/((3𝑛 + 1)) Let P (n) : 1/1.4 + 1/4.7 + 1/7.10 +…….+ 1/((3𝑛 − 2)(3𝑛 + 1)) = 𝑛/((3𝑛 + 1)) For n = 1, L.H.S = 1/1.4 = 1/4 R.H.S = 1/((3(1) + 1)) = 1/((3 + 1)) = 1/4 Hence, L.H.S. = R.H.S , ∴ P(n) is true for n = 1 Assume P(k) is true 1/1.4 + 1/4.7 + 1/7.10 +…….+ 1/((3𝑘 − 2)(3𝑘 + 1)) = 𝑘/((3𝑘 + 1)) We will prove that P(k + 1) is true. R.H.S = ((𝑘 + 1))/((3(𝑘 + 1)+ 1) ) L.H.S = 1/1.4 + 1/4.7 + 1/7.10 +…….+ 1/((3(𝑘 + 1)− 2)(3(𝑘 + 1)+ 1))

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.