


Last updated at May 29, 2018 by Teachoo
Transcript
Ex 4.1,16 Prove the following by using the principle of mathematical induction for all n โ N: 1/1.4 + 1/4.7 + 1/7.10 +โฆโฆ.+ 1/((3๐ โ 2)(3๐ + 1)) = ๐/((3๐ + 1)) Let P (n) : 1/1.4 + 1/4.7 + 1/7.10 +โฆโฆ.+ 1/((3๐ โ 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 , โด P(n) is true for n = 1 Assume P(k) is true 1/1.4 + 1/4.7 + 1/7.10 +โฆโฆ.+ 1/((3๐ โ 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 +โฆโฆ.+ 1/((3(๐ + 1)โ 2)(3(๐ + 1)+ 1))
Ex 4.1
Ex 4.1, 2
Ex 4.1, 3
Ex 4.1, 4
Ex 4.1, 5
Ex 4.1, 6
Ex 4.1, 7 Important
Ex 4.1, 8
Ex 4.1, 9
Ex 4.1, 10
Ex 4.1, 11 Important
Ex 4.1, 12
Ex 4.1, 13 Important
Ex 4.1, 14
Ex 4.1, 15
Ex 4.1, 16 You are here
Ex 4.1, 17
Ex 4.1, 18
Ex 4.1, 19
Ex 4.1, 20
Ex 4.1, 21 Important
Ex 4.1, 22
Ex 4.1, 23 Important
Ex 4.1, 24
About the Author