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The sum of the series: 1/((log)2 4)+1/((...

The sum of the series: `1/((log)_2 4)+1/((log)_4 4)+1/((log)_8 4)++1/((log)_(2n)4)` is `(n(n+1))/2` (b) `(n(n+1)(2n+1))/(12)` (c) `(n(n+1))/4` (d) none of these

A

`(1)/(2)n(n+1)`

B

`(1)/(12)n(n+1)(2n+1)`

C

`(1)/(n(n+1))`

D

`(1)/(4)n(n+1)`.

Text Solution

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The correct Answer is:
D
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MOTION-SEQUENCE & SERIES -Exercise -1 Objective Problems /JEE Main Section -A : AP
  1. The first term of an AP. of consecutive integer is p^2 + 1. The sum of...

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  2. If a1, a2, a3,........ are in A.P. such that a1 + a5 + a10 + a15 + a20...

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  3. The sum of the series: 1/((log)2 4)+1/((log)4 4)+1/((log)8 4)++1/((log...

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  4. The p^(t h) term of an A.P. is aa n dq^(t h) term is bdot Prove that t...

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  5. For a sequence {an}, a1 = 2 and a(n+1)/an=1/3 then sum(r=1)^20 ar is

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  6. If the third term of G.P. is 4, then find the product of first five te...

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  7. If S is the sum to infinite terms of a G.P whose first term is 'a', th...

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  8. alpha ,beta be the roots of the equation x^2 – 3x + a =0 and gamma , d...

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  9. In a G.P. of positive terms if any terms is equal to the sum of next ...

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  10. if 3+1/4(3+d)+1/4^2 (3+2d)+.................oo=8 then the value of d i...

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  11. If x gt 0, and log(2) + log(2)(sqrt(x)) + log(2) (4sqrt(x)) + log(2) (...

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  12. The positive integer n for which 2xx2^2xx+3xx2^3+4xx2^4++nxx2^n=2^(n+1...

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  13. 1+2(1+1//n)+3(1+1//n)^2+…..prop terms , equals.

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  14. If fourth term of an HP is 3/5 and its 8^(th) term is 1/3, then its fi...

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  15. If a1,a2,...an are in H.P then the expression a1a2+a2a3+....+a (n-1)a...

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  16. The sum sum(r=2)^oo1/(r^2-1) is equal to

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  17. Sum of the series S= 1^2-2^2+3^2...-2002^2+2003^2 is

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  18. If 1^2+2^2+3^2+n^2-1015 then the value of n is equal to (A) 13 (B) 14 ...

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  19. If 1/(1^2)+1/(2^2)+1/(3^2)+ tooo=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/(5^...

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  20. v31

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