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(1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...

`(1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=`

A

`2log_(e )2-2`

B

`2-2log_(e )2`

C

`2log_(e )4`

D

`log_(e )4`

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The correct Answer is:
B
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AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(A) (CLASS WORK)
  1. (1)/(1.2)-(1)/(2.3)+(1)/(3.4)-(1)/(4.5)+....=

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  2. (4)/(1.3)-(6)/(2.4)+(12)/(5.7)-(14)/(6.8)+….=

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  3. (1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=

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  4. The 3^(rd), 4^(th), 5^(th) terms in the expansion of log(e )2 are resp...

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  5. sum(n=1)^(oo)(1)/(2n(2n+1))=

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  6. -2[(1)/(8)+(1)/(64)+(1)/(384)+…..oo]=

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  7. If |x| lt 1 then coefficient of x^(n) in log(10)(1-x) is

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  8. log(1+x+x^(2)+...oo)=

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  9. (2)/(1).(1)/(3)+(3)/(2).(1)/(9)+(4)/(3).(1)/(27)+(5)/(4).(1)/(81)+…oo=

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  10. (sqrt(2)-1)/(sqrt(2))+(3-2sqrt(2))/(4)+(5sqrt(2)-7)/(6sqrt(2))+……oo=

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  11. Assertion (A) : If x+(x^(2))/(2)+(x^(3))/(3)+………oo=log((7)/(6)) then...

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  12. If f(x)=(1)/(x+1)+(1)/(2(x+1)^(2))+(1)/(3(x+1)^(3))+…(x gt 1) and f(1...

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  13. y=2x^(2)-1, then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…….oo

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

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

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

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

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

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  19. (1)/(4)+(1)/(3)((1)/(4))^(3)+(1)/(5)((1)/(4))^(5)+…..oo=…….

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  20. 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=

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