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((2n)/(n^(2)+1))+(1)/(3)((2n)/(n^(2)+1))...

`((2n)/(n^(2)+1))+(1)/(3)((2n)/(n^(2)+1))^(3)+(1)/(5)((2n)/(n^(2)+1))^(5)+....=`

A

`log.(n+1)/(n-1)`

B

`log.(n-1)/(n+1)`

C

`log.(1+n)/(1-n)`

D

`log.(1-n)/(1+n)`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. (x)/(x+1)+(1)/(2)((x)/(x+1))^(2)+(1)/(3)((x)/(x+1))^(3)+....=

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  2. (2ax)/(a^(2)+x^(2))+(1)/(3)((2ax)/(a^(2)+x^(2)))^(3)+(1)/(5)((2ax)/(a^...

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  3. ((2n)/(n^(2)+1))+(1)/(3)((2n)/(n^(2)+1))^(3)+(1)/(5)((2n)/(n^(2)+1))^(...

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  4. (1)/(2x-1)+(1)/(3).(1)/((2x-1)^(3))+(1)/(5)(1)/((2x-1)^(5))+....=

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

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  6. (1)/(2n^(2)-1)+(1)/(3(2n^(2)-1)^(3))+(1)/(5(2n^(2)-1)^(5))+....=

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

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

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  9. If |x|lt1 then (1)/(2)x^(2)+(2)/(3)x^(3)+(3)/(4)x^(4)+....=

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  10. (a-1)/(a+1)+(1)/(3)((a-1)/(a+1))^(3)+(1)/(5)((a-1)/(a+1))^(5)+....=

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  11. If |x|lt1 and y=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+..., then x =

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  12. If y=x+(x^(2))/(2)+(x^(3))/(3)+....oo, then x =

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  13. |a|lt1,b=underset(k=1)overset(oo)Sigma(a^(k))/(k)impliesa=

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  14. If y=(1)/(2x^(2)-1)" then "y+(y^(3))/(3)+(y^(5))/(5)+....=

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  15. (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+....=

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  16. (1)/(1.3).(1)/(2)+(1)/(2.4).(1)/(2^(2))+(1)/(3.5).(1)/(2^(3))+....=

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  17. 3x-(5x^(2))/(2)+(9x^(3))/(3)-(17x^(4))/(4)+....+(-1)^(n-1)((2^(n)+1))/...

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  18. 5x-(13)/(2)x^(2)+(35)/(3)x^(3)-(97)/(4)x^(4)+....=

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  19. The coefficient of x^(n) in the expansion of log(e)(1+3x+2x^(2)) is

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  20. The coefficient of x^(n) in the expansion of log (1-5x+6x)^(2) is

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