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Question 10 - Equal - 1 upon addition - Mathematical Induction
Last updated at Dec. 16, 2024 by Teachoo
Mathematical Induction
Concept wise
- Equal - Addition
-
Equal - 1 upon addition
- Equal - Multiplication
- Divisible
- Inequality
Transcript
Question10 Prove the following by using the principle of mathematical induction for all n N: 1/2.5 + 1/5.8 + 1/8.11 + .+ 1/((3 1)(3 + 2)) = /((6 + 4)) Let P (n) : 1/2.5 + 1/5.8 + 1/8.11 + .+ 1/((3 1)(3 + 2)) = /((6 + 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 , P(n) is true for n = 1 Assume P(k) is true 1/2.5 + 1/5.8 + 1/8.11 + .+ 1/((3 1)(3 + 2)) = /((6 + 4)) We will prove that P(k + 1) is true. R.H.S = (( + 1))/((6( + 1) + 4) ) L.H.S = 1/2.5 + 1/5.8 + 1/8.11 + .+ 1/((3( +1) 1)(3( +1)+ 2))
