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The sum of cubes of three successive nat...

The sum of cubes of three successive natural numbers is divisible by

A

6

B

9

C

27

D

8

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. Sum to 30 terms of 3+4+8+9+13+14+18+19+.. is

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  2. The greatest positive integer, which divides (n+1)(n+2)(n+3)(n+4) for ...

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  3. The sum of cubes of three successive natural numbers is divisible by

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  4. Product of 4 consecutive natural numbers is divisible by

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  5. 49^(n)+16 n-1 is divisible by

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  6. If n is a positive integer, then n^(3)+2n is divisible

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  7. If n in N then 3 . 5^(2 n+1)+2^(3 n+1) is divisible by

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  8. If n is a +ve integer, 4^(n)-3 n-1 is divisible by

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  9. The greatest positive integer, which divides (n+1)(n+2)(n+3)(n+4) for ...

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  10. The sum to n terms of the series (1)/(sqrt(1)+sqrt(3))+(1)/(sqrt(3)+...

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  11. The sum of n terms of the series (3)/(1^(2))+(5)/(1^(2)+2^(2))+ (7)/(1...

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  12. If n is odd then the sum of n terms of the series 1^(2)-2^(2)+3^(2)-...

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  13. If log a+log (a^(2)/b)+log (a^(3)/b^(2))+.. .. n terms =(n)/(2)(P log ...

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  14. For a natural number n which one is the correct statement?

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  15. Sum of the series 1+(3^(2))/(2 !)+(3^(4))/(4 !)+(3^(6))/(6 !)+.. . . t...

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  16. 1+(1+2)/(2)+(1+2+3)/(3) +(1+2+3+4)/(4)+.. . to n terms =

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  17. The sum of n terms of the series 1^(2)-2^(2)+3^(2)-4^(2)+5^(2)-6^(2)...

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  18. Sum of the series S=1^(2)-2^(2)+3^(2)-4^(2)+.. ..-(2002)^(2)+(2003)^...

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  19. If S(n)=(1)/(6) n(n+1)(n+2) is the sum to n terms of a series whose n...

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  20. If S(n)=(1)/(6) n(n+1)(n+2) is the sum to n terms of a series whose n...

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