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The cubes of the natural numbers are gro...

The cubes of the natural numbers are grouped as `1^3,(2^3,3^3),(4^3,5^3,6^3)`.... then sum of the number in the nth group is

A

`1/8n^3(n^2+1)(n^2+3)`

B

`1/16n^3(n^2+16)(n^2+12)`

C

`n^3/12(n^2+2)(n^2+4)`

D

none of these

Text Solution

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The correct Answer is:
A
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PATHFINDER-PROGRESSION AND SERIES -QUESTION BANK
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  2. Sum of n terms of the series (2n-1)+2(2n-3)+3(2n-5)+.... is

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  3. The cubes of the natural numbers are grouped as 1^3,(2^3,3^3),(4^3,5^3...

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  6. If a,b,c are three distinct positive real number such that a^2+b^2+c^2...

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  7. The sum of the series 1^3 - 2^3 + 3^3 - ....+ 9^3=

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  10. The sum of the first n terms of the series 1^2+2.2^2+3^2+2.4^2+5^2+2.6...

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  11. Let a1 , a2 , a3,.... be terms of an A.P. if (a1 + a2 +....+ ap)/(a1 +...

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  12. If a1,a2,.....an are in H.P., then the expression a1a2 + a2a3 + ... + ...

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  13. If the sum of first n natural numbers is 1/5 times the sum of their sq...

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  14. log3 2 , log6 2 and log12 2 are in

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  15. If x be the AM and y,z be two GM's between two positive numbers, then ...

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  16. If In (a + c), In(c - a) , In(a - 2b + c) are in A.P., then

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  18. Suppose that F(n + 1) =(2F(n) + 1)/2 for n = 1,2,3,,,, and F(1) = 2. T...

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  19. The series of natural number is divided into groups 1 , 2, 3, 4,.........

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  20. sum(i = 1)^n sum(j = 1)^i sum(k = 1)^j 1 is equal to

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