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Ex 4.1,10 - Prove 1/2.5 + 1/5.8 + 1/8.11 + .. + 1/(3n-1)(3n+2) - Equal - 1 upon addition

  1. Chapter 4 Class 11 Mathematical Induction
  2. Serial order wise
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Ex 4.1,10 Prove the following by using the principle of mathematical induction for all n โˆˆ N: 1/2.5 + 1/5.8 + 1/8.11 +โ€ฆโ€ฆ.+ 1/((3๐‘› โˆ’ 1)(3๐‘› + 2)) = ๐‘›/((6๐‘› + 4)) Let P (n) : 1/2.5 + 1/5.8 + 1/8.11 +โ€ฆโ€ฆ.+ 1/((3๐‘› โˆ’ 1)(3๐‘› + 2)) = ๐‘›/((6๐‘› + 4)) For n = 1, L.H.S = 1/2.5 = 1/10 R.H.S = 1/((6(1) + 4)) = 1/((6 + 4)) = 1/10 Hence, L.H.S. = R.H.S , โˆด P(n) is true for n = 1 Assume P(k) is true 1/2.5 + 1/5.8 + 1/8.11 +โ€ฆโ€ฆ.+ 1/((3๐‘˜ โˆ’ 1)(3๐‘˜ + 2)) = ๐‘˜/((6๐‘˜ + 4)) We will prove that P(k + 1) is true. R.H.S = ((๐‘˜ + 1))/((6(๐‘˜ + 1) + 4) ) L.H.S = 1/2.5 + 1/5.8 + 1/8.11 +โ€ฆโ€ฆ.+ 1/((3(๐‘˜+1) โˆ’ 1)(3(๐‘˜+1)+ 2))

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