Answer
Step by step text solution for Prove the following by induction. 1 + 2+ 3+….+ n = n(n+1)//2 by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.
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MBD PUBLICATION-PRINCIPLES OF MATHEMATICAL INDUCTION -QUESTION BANK
- Prove the following by induction. 1 + 2+ 3+….+ n = n(n+1)//2
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- Prove the following by induction. 1^2 + 2^2 + ….+ n^2 = n(n+1)(2n+1)//...
06:51
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- Prove the following by induction. 1 + r + r^2 +…..+ r^n = (r^(n+1) -1)...
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- 5^n -1 is divisible by 4.
03:28
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- 7^(2n) + 2^(3n-3) 3^(n-1) is divisible by 25 for any natural number n ...
07:34
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- 7.5^(2n-1) + 2^(3n+1) is divisible by 17 for every natural n ge 1.
07:59
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- 4^(n+1) + 15n + 14 is divisible by 9 for every natural number n ge 0.
06:06
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- 3^(2(n-1)) + 7 is divisible by 8 for every natural n ge 2.
06:12
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- 5^(2(n-4) -6n + 32 is divisible by 9 for every natural number n ge 5.
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- 1/1.2 + 1/2.3 +…..+ 1/(n(n+1)) = n/(n+1)
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- 1.3 + 2.4 + 3.5 + …… + n(n+2) =( n(n+1)(2n+7))/6
07:40
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- x^n - y^n = (x-y) (x^(n-1) + x^(n-2) y + … + xy^(n-2) + y^(n-1)) , x,y...
07:38
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- 1 + 3 + 5 +……+ (2n -1) = n^2
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- 2^n gt n , n is a natural number.
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- (1. 2. 3 … n)^3 gt 8 (1^3 + 2^3 + 3^3 + …+ n^3), for n gt 3
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- 1/(n+1) + 1/(n+2)+…..+ 1/(3n+1) gt 1 for every positive integer n.
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