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The sum of the series (1)/(2)((1)/(5))^(...

The sum of the series `(1)/(2)((1)/(5))^(2)+(2)/(3)((1)/(5))^(3)+(3)/(4)((1)/(5))^(4)+...` is

A

`(1)/(4)+log_(e)((4)/(5))`

B

`(1)/(3)+log_(e)((2)/(3))`

C

`(1)/(2)+log_(e)((3)/(2))`

D

none of these

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Verified by Experts

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

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  2. (1)/(5)+(1)/(2.5^(2))+(1)/(3.5^(3))+(1)/(4.5^(4))+.......=

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  3. The sum of the series (1)/(2)((1)/(5))^(2)+(2)/(3)((1)/(5))^(3)+(3)/(4...

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  4. (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+.....

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  5. (1)/(2)+(3)/(2).(1)/(4)+(5)/(3).(1)/(8)+(7)/(4).(1)/(16)+....=

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

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  7. (a-b)/(a)+(1)/(2)((a-b)/(a))^(2)+(1)/(3)((a-b)/a)^(3)+....=

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  8. (a-1)-(1)/(2)(a-1)^(2)+(1)/(3)(a-1)^(3)-(1)/(4)(a-1)^(4)+...=

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

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  10. If S=((b-1)-(1)/(2)(b-1)^(2)+(1)/(3)(b-1)^(3)-....)/((a-1)-(1)/(2)(a-1...

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

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

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  13. (2ax)/(a^(2)+x^(2))+(1)/(3)((2ax)/(a^(2)+x^(2)))^(3)+(1)/(5)((2ax)/(a^...

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  14. ((2n)/(n^(2)+1))+(1)/(3)((2n)/(n^(2)+1))^(3)+(1)/(5)((2n)/(n^(2)+1))^(...

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  15. (1)/(2x-1)+(1)/(3).(1)/((2x-1)^(3))+(1)/(5)(1)/((2x-1)^(5))+....=

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  16. (1)/(2x+1)+(1)/(3)(1)/((2x+1)^(3))+(1)/(5)(1)/((2x+1)^(5))+....=

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  17. (1)/(2n^(2)-1)+(1)/(3(2n^(2)-1)^(3))+(1)/(5(2n^(2)-1)^(5))+....=

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

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

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

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