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Last updated at Feb. 15, 2020 by Teachoo

Ex 4.1,16 Prove the following by using the principle of mathematical induction for all n β N: 1/1.4 + 1/4.7 + 1/7.10 +β¦β¦.+ 1/((3π β 2)(3π + 1)) = π/((3π + 1)) Let P (n) : 1/1.4 + 1/4.7 + 1/7.10 +β¦β¦.+ 1/((3π β 2)(3π + 1)) = π/((3π + 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 , β΄ P(n) is true for n = 1 Assume P(k) is true 1/1.4 + 1/4.7 + 1/7.10 +β¦β¦.+ 1/((3π β 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 +β¦β¦.+ 1/((3(π + 1)β 2)(3(π + 1)+ 1))