Question 3 - Equal - 1 upon addition - Mathematical Induction

Last updated at July 24, 2026 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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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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