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(a-1)/(a+1)+(1)/(3)((a-1)/(a+1))^(3)+(1)...

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

A

`loga`

B

`(1)/(2)loga`

C

`2loga`

D

`log(1//a)`

Text Solution

Verified by Experts

The correct Answer is:
B
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(1)/(4)+(1)/(3)((1)/(4))^(3)+(1)/(5)((1)/(4))^(5)+…..oo=…….

2[((1)/(2))+(1)/(3)((1)/(2))^(3)+(1)/(5)((1)/(2))^(5)+...]=

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

2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...] =

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

I:2[((1)/(3))+(1)/(3)((1)/(3))^(3)+(1)/(5)((1)/(3))^(5)+...]=log_(e)2 II:2[((1)/(2))+(1)/(3)((1)/(2))^(3)+(1)/(5)((1)/(2))^(5)+...]=log_(e)2

If (3)/(4)+(1)/(3)((3)/(4))^(3)+(1)/(5)((3)/(4))^(5)+....=log_(e)a,(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/(7.3^(7))+....=log_(e)b, 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=log_(e)c then the ascending order of a, b, c is

(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/(7.3^(7))+....=

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

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

DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. log(1+x+x^(2)+...oo)=

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

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

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

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

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

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

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

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  9. (1)/(1.3).(1)/(2)+(1)/(2.4).(1)/(2^(2))+(1)/(3.5).(1)/(2^(3))+....=

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  10. 3x-(5x^(2))/(2)+(9x^(3))/(3)-(17x^(4))/(4)+....+(-1)^(n-1)((2^(n)+1))/...

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  11. 5x-(13)/(2)x^(2)+(35)/(3)x^(3)-(97)/(4)x^(4)+....=

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

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

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  14. If n=3m then the coefficient of x^(n) in the expansion of log(1+x+x^(2...

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  15. If n=3m then the coefficient of x^(n) in the expansion of log(1+x+x^(2...

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  16. The expansion of log.(1+x+x^(2))/(1-x+x^(2)) as ascending powers of x ...

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  17. If |x|lt1, the coefficient of x^(3) in the expansion of log(1+x+x^(2))...

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  18. If x is very small and neglecting x^(3) and higher powers of x then th...

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  19. (x)/(1.2)+(x^(2))/(3.4)+(x^(3))/(5.6)+....=

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  20. underset(n=1)overset(oo)sum(x^(n))/(n+2)=

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