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The expansion of log.(1+x+x^(2))/(1-x+x^...

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

A

`x-(2)/(3)x^(3)+(x^(5))/(5)+(x^(7))/(7)-(2)/(9)x^(9)....`

B

`x+(2)/(3)x^(3)+x^(5)/(5)+(x^(7))/(7)+(2)/(9)x^(9)....`

C

`2[x-(2)/(3)x^(3)+(x^(5))/(5)+(x^(7))/(7)-(2)/(9)x^(9)....]`

D

`2[x+(2)/(3)x^(3)+(x^(5))/(5)+(x^(7))/(7)+(2)/(9)x^(9)....]`

Text Solution

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The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. 5x-(13)/(2)x^(2)+(35)/(3)x^(3)-(97)/(4)x^(4)+....=

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

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

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

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

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

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

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

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

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

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

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  12. sin^(2)theta+(1)/(2)sin^(4)theta+(1)/(3)sin^(6)theta+....=

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  13. cos^(2)theta+(1)/(2)cos^(4)theta+(1)/(3)cos^(6)theta+....=

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  14. tan^(2)theta-(1)/(2)tan^(4)theta+(1)/(3)tan^(6)theta-(1)/(4)tan^(8)the...

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  15. costheta+(1)/(3)cos^(3)theta+(1)/(5)cos^(5)theta+....=

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  16. sin2theta+(1)/(3)sin^(3)2theta+(1)/(5)sin^(5)2theta+....=

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  17. cos2theta+(1)/(3)cos^(3)2theta+(1)/(5)cos^(5)2theta+....=

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  18. tantheta+(1)/(3)tan^(3)theta+(1)/(5)tan^(5)theta+....=

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  19. The sum of the series log(4)2-log(8)2+log(16)2-.... is

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  20. If x,y,z are three consecutive positive integers then (1)/(2)log(e)x...

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