Ex 4.1, 16 - Prove 1/1.4 + 1/4.7 ... + 1/(3n-2)(3n+1) = n/(3n+1) - Equal - 1 upon addition

  1. Chapter 4 Class 11 Mathematical Induction
  2. Serial order wise
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Ex 4.1,16 Prove the following by using the principle of mathematical induction for all n โˆˆ N: 1/1.4 + 1/4.7 + 1/7.10 +โ€ฆโ€ฆ.+ 1/((3๐‘› โˆ’ 2)(3๐‘› + 1)) = ๐‘›/((3๐‘› + 1)) Let P (n) : 1/1.4 + 1/4.7 + 1/7.10 +โ€ฆโ€ฆ.+ 1/((3๐‘› โˆ’ 2)(3๐‘› + 1)) = ๐‘›/((3๐‘› + 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 , โˆด P(n) is true for n = 1 Assume P(k) is true 1/1.4 + 1/4.7 + 1/7.10 +โ€ฆโ€ฆ.+ 1/((3๐‘˜ โˆ’ 2)(3๐‘˜ + 1)) = ๐‘˜/((3๐‘˜ + 1)) We will prove that P(k + 1) is true. R.H.S = ((๐‘˜ + 1))/((3(๐‘˜ + 1)+ 1) ) L.H.S = 1/1.4 + 1/4.7 + 1/7.10 +โ€ฆโ€ฆ.+ 1/((3(๐‘˜ + 1)โˆ’ 2)(3(๐‘˜ + 1)+ 1))

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