Question 17 - Equal - 1 upon addition - Mathematical Induction

Last updated at Dec. 16, 2024 by

Ex 4.1, 17 - Prove 1/3.5 + 1/5.7 + 1/7.9 .. + 1/(2n + 1)(2n + 3) - Equal - 1 upon addition

Ex 4.1, 17 - Chapter 4 Class 11 Mathematical Induction - Part 2
Ex 4.1, 17 - Chapter 4 Class 11 Mathematical Induction - Part 3
Ex 4.1, 17 - Chapter 4 Class 11 Mathematical Induction - Part 4

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Transcript

Question17 Prove the following by using the principle of mathematical induction for all n N: 1/3.5 + 1/5.7 + 1/7.9 + .+ 1/((2 + 1)(2 + 3)) = /(3(2 + 3)) Let P (n) : 1/3.5 + 1/5.7 + 1/7.9 + .+ 1/((2 + 1)(2 + 3)) = /(3(2 + 3)) For n = 1, L.H.S = 1/3.5 = 1/15 R.H.S = 1/(3(2(1) + 3)) = 1/(3(2 +3)) = 1/(3 5) = 1/15 Hence, L.H.S. = R.H.S , P(n) is true for n = 1 Assume P(k) is true 1/3.5 + 1/5.7 + 1/7.9 + .+ 1/((2 + 1)(2 + 3)) = /(3(2 + 3)) We will prove that P(k + 1) is true. R.H.S = (( + 1))/3(2( + 1) + 3) L.H.S = 1/3.5 + 1/5.7 + 1/7.9 + .+ 1/((2( + 1) + 1)(2( + 1) + 3))

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