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(5)/(1.2.3)+(7)/(3.4.5)+(9)/(5.6.7)+.......

`(5)/(1.2.3)+(7)/(3.4.5)+(9)/(5.6.7)+....=`

A

`log_(e)((8)/(e))`

B

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

C

`log_(e)((6)/(5))`

D

`2-log_(e)2`

Text Solution

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The correct Answer is:
A
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(1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+....

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The sum of the series (1)/(1.3.5)+(1)/(3.5.7)+(1)/(5.7.9)+... is

(3)/(2!)+(5)/(3!)+(7)/(4!)+(9)/(5!)+....=

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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. (1)/(1.3)+(1)/(2.5)+(1)/(3.7)+(1)/(4.9)+...=

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  2. (1)/(1.2.3)+(1)/(3.4.5)+(1)/(5.6.7)+....

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  3. (5)/(1.2.3)+(7)/(3.4.5)+(9)/(5.6.7)+....=

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  4. The sum of the series (1)/(1.3.5)+(1)/(3.5.7)+(1)/(5.7.9)+... is

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  5. Sum of the series (1)/(4.5.6)+(1)/(5.6.7)+(1)/(6.7.8)+... upto oo is

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  6. (1)/(1.3)+(1)/(2)((1)/(3.5))+(1)/(3)((1)/(5.7))+....=

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  7. (2)/(3)+(1)/(2)((2)/(3))^(2)+(1)/(3)((2)/(3))^(3)+....=

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  8. (1)/(5)+(1)/(2.5^(2))+(1)/(3.5^(3))+(1)/(4.5^(4))+.......=

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

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  10. (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+.....

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  11. (1)/(2)+(3)/(2).(1)/(4)+(5)/(3).(1)/(8)+(7)/(4).(1)/(16)+....=

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

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

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

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

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

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

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

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  19. (2ax)/(a^(2)+x^(2))+(1)/(3)((2ax)/(a^(2)+x^(2)))^(3)+(1)/(5)((2ax)/(a^...

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

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