Last updated at Dec. 8, 2016 by Teachoo

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Example 3 For all n โฅ 1, prove that 1/1.2 + 1/2.3 + 1/3.4 +โฆโฆ.+ 1/(๐(๐ + 1)) = 1/(๐ + 1) Let P (n) : 1/1.2 + 1/2.3 + 1/3.4 +โฆโฆ.+ 1/(๐(๐ + 1)) = 1/(๐ + 1) For n=1, L.H.S = 1/1.2 = 1/2 R.H.S = 1/(1+1) = 1/2 Hence, L.H.S. = R.H.S , โด P(n) is true for n = 1 Assume P(k) is true 1/1.2 + 1/2.3 + 1/3.4 +โฆโฆ.+ 1/(๐(๐+1)) = ๐/(๐+1) We will prove that P(k + 1) is true. R.H.S = ((k + 1))/(((k + 1)+ 1) ) L.H.S =1/1.2 + 1/2.3 + 1/3.4 +โฆโฆ.+ 1/((k + 1)((k + 1)+ 1)) โด By the principle of mathematical induction, P(n) is true for n, where n is a natural number

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.