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Ex 4.1, 16 - Chapter 4 Class 11 Mathematical Induction

Last updated at March 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

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Transcript

Ex 4.1,16 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 βˆ’ 2)(3𝑛 + 1)) = 𝑛/((3𝑛 + 1)) Let P (n) : 1/1.4 + 1/4.7 + 1/7.10 +…….+ 1/((3𝑛 βˆ’ 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/((3π‘˜ βˆ’ 2)(3π‘˜ + 1)) = π‘˜/((3π‘˜ + 1)) We will prove that P(k + 1) is true. R.H.S = ((π‘˜ + 1))/((3(π‘˜ + 1)+ 1) ) L.H.S = 1/1.4 + 1/4.7 + 1/7.10 +…….+ 1/((3(π‘˜ + 1)βˆ’ 2)(3(π‘˜ + 1)+ 1))

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