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Statement -1 For each natural number n,(...

Statement -1 For each natural number `n,(n+1)^(7)-n^7-1` is divisible by 7.
Statement -2 For each natural number `n,n^7-n` is divisible by 7.

A

1

B

2

C

3

D

4

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OBJECTIVE RD SHARMA ENGLISH-MATHEMATICAL INDUCTION -Exercise
  1. Statement -1 For each natural number n,(n+1)^(7)-n^7-1 is divisible by...

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  2. AA n in N, 49^n+16n-1 is divisible by (A) 64 (B) 49 (C) 132 (D) ...

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  3. show that n(n^2 -1), is divisible by 24 if n is an odd positive number...

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  4. For all n in N, 7^(2n)-48n-1 is divisible by

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  5. Prove the following by the principle of mathematical induction:\ 5^...

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  6. For all n in N, n^(3)+2n is divisible by

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  7. For all n in N, 4^(n)-3n-1 is divisible by

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  8. For all n in N, 3^(3n)-26^(n)-1 is divisible by

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  9. If n in N, then 3^(2n)+7 is divisible by

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  10. For all n in N, 3n^(5) + 5n^(3) + 7n is divisible by

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  11. Find the sum of first n terms of the following series: 3+7+13+21+31+ d...

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  12. n^(th) term of the series 4+14+30+52+ .......=

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  13. 3 + 13 + 29 + 51 + 79+… to n terms =

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  14. Find the sum of the following series to n term: 1^3+3^3+5^3+7^3+ dot

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  15. If 10^(n)+3*4^(n+2) + is divisible by 9, for all ninN, then the least ...

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  16. If x^n-1 is divisible by x-k then the least positive integral value of...

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  17. If a,b are distinct rational numbers, then for all n in N the number a...

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  18. If n is an odd positive integer, then a^(n)+b^(n) is divisible by

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  19. If n is an even positive integer, then a^(n)+b^(n) is divisible by

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  20. For all n in N, (n^(5))/(5)+(n^(3))/(3)+(7n)/(15) is

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  21. The sum of n terms of the series 1+(1+a)+(1+a+a^(2))+(1+a+a^(2)+a^(...

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