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

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

A

3

B

5

C

10

D

15

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The correct Answer is:
D
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OBJECTIVE RD SHARMA ENGLISH-MATHEMATICAL INDUCTION -Exercise
  1. For all n in N, 3^(3n)-26^(n)-1 is divisible by

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

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

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

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

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  6. 3 + 13 + 29 + 51 + 79+… to n terms =

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

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

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

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

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

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

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

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

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

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  16. Using mathematical induction , to prove that 7^(2n)+2^(3n-3). 3^(...

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

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  18. For each n in N, n(n+1) (2n+1) is divisible by

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  19. The sum of the cubes of three consecutive natural numbers is divisible...

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  20. ((n+2)!)/((n-1)!) is divisible by

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