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

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

A

`(x)/(1-x)+log(1-x)`

B

`(x)/(1-x)+log(1+x)`

C

`(x)/(1+x)+log(1+x)`

D

`(x)/(1+x)+log(1-x)`

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The correct Answer is:
A
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Find Lt_(xto1)(2x^(2)+3x+4) .

A : (1)/(2)-(1)/(2).(1)/(2^(2))+(1)/(3).(1)/(2^(3))-(1)/(4).(1)/(2^(4))+....=log_(e)((3)/(2)) R : log_(e)(1+x)=x-(x^(2))/(2)+(x^(3))/(3)-(x^(4))/(4)+...

DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. If xgt0 then (x-1)/(x+1)+(1)/(2)(x^(2)-1)/((x+1)^(2))+(1)/(3)(x^(3)-1)...

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

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

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

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

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

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

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

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

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  10. (1)/(1.3).(1)/(2)+(1)/(2.4).(1)/(2^(2))+(1)/(3.5).(1)/(2^(3))+....=

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  11. 3x-(5x^(2))/(2)+(9x^(3))/(3)-(17x^(4))/(4)+....+(-1)^(n-1)((2^(n)+1))/...

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  12. 5x-(13)/(2)x^(2)+(35)/(3)x^(3)-(97)/(4)x^(4)+....=

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

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

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

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

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

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

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

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