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If the natural numbers are divided into ...

If the natural numbers are divided into the groups `(1),(2,3),(4,5,6),(7,8,9,10) ..` then the sum of the elements of `25^(th )` group is

A

7820

B

7850

C

7825

D

7840

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The correct Answer is:
D
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HIMALAYA PUBLICATION-MATHEMATICAL INDUCTION AND SUMMATION OF SERIES-Question Bank
  1. If the sum of n terms of the series : (1)/( 1^(3)) +( 1+2)/( 1^(3) +...

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  2. Sum of 25 terms of the series 1 . 3+2 . 5+3 . 7+.., is

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  3. If the natural numbers are divided into the groups (1),(2,3),(4,5,6),(...

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  4. If (sum n^(3))(sum n)=(sum n^(2))^(2), then

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  5. 4^(3)+5^(3)+6^(3)+.. .+10^(3)=

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  6. 3+5+7+ …..to n^(th) term is

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  7. ((1)/(2) . (2)/(2))/(1^(3))+((2)/(3) . (3)/(2))/(1^(3)+2^(3)) +((3)/(2...

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  8. The 10^(th ) term of the series 3+13+29+51+79+.. ..

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  9. Sum to 30 terms of 3+4+8+9+13+14+18+19+.. is

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

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

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  12. Product of 4 consecutive natural numbers is divisible by

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  13. 49^(n)+16 n-1 is divisible by

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

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

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

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

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

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

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

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