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

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

A

3

B

8

C

9

D

11

Text Solution

Verified by Experts

The correct Answer is:
C
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OBJECTIVE RD SHARMA-MATHEMATICAL INDUCTION -Exercise
  1. 5^(2n)-1 is divisible by 24 for all n epsilon N

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

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

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

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

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

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

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

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  9. 3 + 13 + 29 + 51 + 79+… to n terms =

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  10. Sum of n terms of the following series1^3+3^3+5^3+7^3+

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  11. If 10^n+3xx4^(n+2)+lambda is divisible by 9 or all n N , then the lea...

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

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

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

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

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

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

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  18. If 3+5+9+17+33+… to n terms =2^(n+1)+n-2, then nth term of LHS, is

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  19. 7^(2n)+2^(3n-3)*3^(n-1) is divisible by 25

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  20. Prove that for n in N ,10^n+3. 4^(n+2)+5 is divisible by 9 .

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