Question 3 - Equal - 1 upon addition - Mathematical Induction

Last updated at April 16, 2024 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

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Transcript

Question3: 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)))

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo