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Sum of the series (1)/(2)((1)/(2)+(1)/(3...

Sum of the series `(1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^(2)))+(1)/(6)((1)/(2^(3))+(1)/(3^(3)))-...` is

A

`log_(e )3`

B

`(1)/(2)log_(e )2`

C

`(1)/(2)"log"_(e )(3)/(2)`

D

`"log"_(e )(2)/(3)`

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Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-LOGARITHMIC SERIES -EXERCISE - II(B) (HOME WORK)
  1. (1)/(2.3)+(1)/(4.5)+(1)/(6.7)+……oo=

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  2. (1)/(1.2)+(1)/(3.4)+(1)/(5.6)+....

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  3. Sum of the series (1)/(2)((1)/(2)+(1)/(3))-(1)/(4)((1)/(2^(2))+(1)/(3^...

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  4. -((4)/(5)+(4^(2))/(5^(2).2)+(4^(3))/(5^(3).3)+(4^(4))/(5^(4).4)+……oo)=

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  5. y=(x^(3)+(x^(6))/(2)+(x^(9))/(3)+……) then

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  6. If |x|lt 1, tnen the coefficient of x^(5) in the expansion of (1-x)log...

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  7. (1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=

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  8. (x)/(x+1)+(1)/(2)((x)/(x+1))^(2)+(1)/(3)((x)/(x+1))^(3)+....=

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  9. The 3^(rd) term in log((1)/(1-x)) is

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  10. n^(th) term of log(e )(6//5) is

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  11. 2log x-log(x+1)-log(x-1)=

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  12. If x^(2)y=2x-y then y^(2)+(y^(4))/(2)+(y^(6))/(3)+…oo=

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  13. If higher powers of x^(2) are neglected, then the value of log(1+x^(2)...

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  14. If (1)/(n+1)+(1)/(2(n+1)^(2))+(1)/(3(n+1)^(3))+….= lambda((1)/(n)-(1...

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  15. Assertion (A) : coefficient x^(n) in log(1+x) is ((-1)^(n-1))/(n) when...

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  16. Observe the following lists. {:("LIST - I","LIST - II"),((A) 8^(th)"...

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  17. x+(x^(3))/(3)+(x^(5))/(5)+(x^(7))/(7)+….oo=

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  18. 2[7^(-1)+3^(-1)7^(-3)+5^(-1)7^(-5)+…]=

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  19. 2[(1)/(2x+1)+(1)/(3*(2x+1)^(3))+(1)/(5*(2x+1)^(5))+…..oo]=

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  20. (2x)/(x^(2)+1)+(1)/(3)((2x)/(x^(2)+1))^(3) +(1)/(5)((2x)/(x^(2)+1))^(5...

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