HomePrinciple of mathematical induction Principle of mathematical induction Section- 1 byAayushi Bindal •June 14, 2021 0 1.For all n∈N, 3n5 + 5n³ + 7n is divisible by 1. None 2. 10 3. 5 4. 15 2. {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} = 1. 1/(n + 1) for all n ∈ R 2. 1/(n + 1) for all n ∈ N. 3. n/(n + 1) for all n ∈ N. 4. n/(n + 1) for all n ∈ R 3.For all n ∈ N, 32n + 7 is divisible by 1. 8 2. 4 3. 3 4. None of these 4. The sum of the series 1 + 2 + 3 + 4 + 5 + ………..n is 1. n/2 2.(n + 1)/2 3. n(n + 1)/2 4. None of these 5.The sum of the series 1² + 2² + 3² + ……….. n² is 1.n(n + 1) (2n + 1)/3 2. n(n + 1) (2n + 1)/6 3. n(n + 1) (2n + 1)/2 4. None of these 6.For all positive integers n, the number n(n² − 1) is divisible by: 1. 5 2. 3 3.6 4. 24 7.If n is an odd positive integer, then aⁿ + bⁿ is divisible by : 1. a – b 2. a+b 3. a² + b² 4. None of these. 8.n(n + 1) (n + 5) is a multiple of ____ for all n ∈ N 1. 3 2. 2 3. 6 4. None of these 9.For any natural number n, 7ⁿ – 2ⁿ is divisible by 1. 2 2. 4 3. 8 4. 5 10.The sum of the series 1³ + 2³ + 3³ + ………..n³ is 1. {n(n + 1)/2}² 2. n(n + 1)/2 3. {n/2}² 4. None of these 11.(1² + 2² + …… + n²) _____ for all values of n ∈ N 1. less than n³/3 2. None of these 3. = n³/3 4. > n³/3 12. {1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1) (2n + 3)} = 1. n/(2n + 3) 2. n/{2(2n + 3)} 3. n/{3(2n + 3)} 4. n/{4(2n + 3)} 13. If n is an odd positive integer, then aⁿ + bⁿ is divisible by : 1. a-b 2. a² + b² 3. a+b 4. None of these 14.(2 ∙ 7N + 3 ∙ 5N – 5) is divisible by ……….. for all N ∈ N 1. 21 2. 28 3. 25 4. 29 15. For all n∈N, 52n − 1 is divisible by 1. 24 2. 34 3. 36 4. None of the above Tags: Principle of mathematical induction Facebook Twitter