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If x,y,z are three consecutive positive integers then
`(1)/(2)log_(e)x+(1)/(2)log_(e)z+(1)/(2xz+1)+(1)/(3)((1)/(2xz+1))^(3)+....=`

A

`log_(a )y`

B

`log_(e )(1//y)`

C

`log_(e )y`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(A) (CLASS WORK)
  1. y=2x^(2)-1, then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…….oo

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  2. If |a| lt 1, b = sum(k=1)^(oo) (a^(k))/(k) rArr a=

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  3. If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)...

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  4. Statement-I : ((x-y)/(x))+(1)/(2)((x-y)/(x))^(2)+(1)/(3)((x-y)/(x))^...

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  5. Statement-I : log(1+x+x^(2)+…)=x+(x^(2))/(2)+(x^(3))/(3)+(x^(4))/(4)...

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  6. Observe the following lists {:("List-I","List-II"),((A) 1-(1)/(2)+(...

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  7. (1)/(4)+(1)/(3)((1)/(4))^(3)+(1)/(5)((1)/(4))^(5)+…..oo=…….

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  8. 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=

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  9. If y+(y^(3))/(3)+(y^(5))/(5)+…oo=2[x+(x^(3))/(5)+(x^(5))/(5)+…oo] then

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  10. sin2theta+(1)/(3)sin^(3)2theta+(1)/(5)sin^(5)2theta+....=

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  11. If 0 lt y lt 2^(1//3) and x(y^(3)-1)=1 then (2)/(x)+(2)/(3x^(3))+(2)...

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  12. If x,y,z are three consecutive positive integers then (1)/(2)log(e)x...

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  13. sum(n=1)^(oo)(1)/(2n-1)*x^(2n)=

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  14. If 0 lt y lt 1, then sum(n=1)^(oo)(1)/(2n-1)*y^(n+1)=……

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  15. If log(e )((1+x)/(1-x))=a(0)+a(1)x+a(2)x^(2)+…oo then a(1), a(3), a(5)...

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  16. Assertion (A) : The coefficient of of x^(5) in the expansion log(e ) (...

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  17. If n is a multiple of 3, then coefficient of x^(n) in log(1+x+x^(2)) i...

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  18. If n is a not a multiple of 3, then the coefficient of x^(n) in the ex...

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  19. Match the following for coefficient of x^(n) in log(e )(1+x+x^(2)) ...

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  20. If |x|lt1, the coefficient of x^(3) in the expansion of log(1+x+x^(2))...

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