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

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

A

`log(1+4x+3x^(2))`

B

`log_(e)(1+3x+2x^(2))`

C

`log(1+5x+6x^(2))`

D

`log_(e)(1+6x+5x^(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+....=

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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