1. Chapter 4 Class 11 Mathematical Induction (Deleted)
  2. Serial order wise
  3. Ex 4.1

Ex 4.1, 3 - Chapter 4 Class 11 Mathematical Induction (Deleted)

Last updated at Feb. 15, 2020 by

Ex 4.1, 3 - Prove by induction 1 + 1/(1 + 2) + 1/(1 + 2 + 3) + .. - Equal - 1 upon addition

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

  1. Chapter 4 Class 11 Mathematical Induction (Deleted)
  2. Serial order wise

    3. Ex 4.1

    Examples →

Transcript

Ex 4.1,3: Prove the following by using the principle of mathematical induction for all n N: 1 + 1/((1 + 2)) + 1/((1 + 2 + 3)) + .. + 1/((1 + 2 + 3 + . )) = 2 /(( + 1)) Let P (n) : 1 + 1/((1 + 2)) + 1/((1 + 2 + 3)) + .. + 1/((1 + 2 + 3 + . )) = 2 /(( + 1)) For n = 1, L.H.S = 1 R.H.S = 2(1)/(((1) +1)) = 2/((2)) = 1 Hence, L.H.S. = R.H.S , P(n) is true for n = 1 Assume P(k) is true 1 + 1/((1 + 2)) + 1/((1 + 2 + 3)) + .. + 1/((1 + 2 + 3 + + )) = 2 /(( + 1)) We will prove that P(k + 1) is true. R.H.S = 2( + 1)/((( + 1) + 1) ) L.H.S = 1 + 1/((1 + 2)) + 1/((1 + 2 + 3)) + .. + 1/((1 + 2 + 3 + +( + 1)))

Chapter 4 Class 11 Mathematical Induction (Deleted)
Serial order wise

About the Author

Davneet Singh's photo - Teacher, Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.