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If 2^(3)+4^(3)+6^(3)+.. .+(2 n)^(3)=k n^...

If `2^(3)+4^(3)+6^(3)+.. .+(2 n)^(3)=k n^(2)(n+1)^(2)` then k=

A

`(1)/(2)`

B

1

C

`(3)/(2)`

D

2

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

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  2. If a(k)=(1)/(k(k+1)) for k=1,2,3, .., n, then (sum(k=1)^(n) a(k))^(...

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  3. If 2^(3)+4^(3)+6^(3)+.. .+(2 n)^(3)=k n^(2)(n+1)^(2) then k=

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  4. Find the sum of integers from 1 to 100 that are divisible by 2 or 5.

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  5. If t(n)=(1)/(4)(n+2)(n+3) , n=1,2,3, .. then (1)/(t(1))+(1)/(t(2))...

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  6. sum(k=1)^(5) (1^(3)+2^(3)+.. ..+k^(3))/(1+3+5+.. ..+(2 k-1))=

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  7. For all integers n ge 1, which of the following is divisible by 9

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  8. The sum of first n terms of the series 1^(2) + 2.2^(2) +3^(2) + 2. 4...

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  9. If S(n)=(1)/(6.11)+(1)/(11.16)+(1)/(16.21)+ ….. to n terms, then 6S(n)...

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  10. 1/(2*5)+1/(5*8)+1/(8*11)+............1/((3n-1)(3n+2))=n/((6n+4)) foral...

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  11. Sum to n terms of the series (1)/(2 . 5) +(1)/(5 . 8)+(1)/(8 . 11)+..=

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

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  13. The number (49^(2)-4)(49^(3)-49) is divisible by

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

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  15. 1+3+5+7+..+29+30+31+32+..+60=

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  16. The sum of n terms of the series 1+(1+3)+(1+3+5)+.. .. .. is

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  17. 1+(3)/(2)+(5)/(2^(2))+(7)/(2^(3))+.. .. to infty=

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  18. sum(i=1)^(n) sum(j=1)^(i)sum(k=1)^(j) 1 equals :

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  19. The sum 1^(2)+1+2^(2)+2+3^(2)+3+..+n^(2)+n is

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  20. The sum to infinity of the series : 1+ ( 2)/( 3) + ( 6)/( 3^(2)) +(...

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