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

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

A

`y+(y^(2))/(2)+(y^(3))/(3)+...`

B

`y-(y^(2))/(2)+(y^(3))/(3)-(y^(4))/(4)+...`

C

`y+(y^(2))/(2!)+(y^(3))/(3!)+...`

D

`y-(y^(2))/(2!)+(y^(3))/(3!)-(y^(4))/(4!)+...`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1B
  1. If |x|lt1 then (1)/(2)x^(2)+(2)/(3)x^(3)+(3)/(4)x^(4)+....=

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

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

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

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

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

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

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  8. (1)/(1.3).(1)/(2)+(1)/(2.4).(1)/(2^(2))+(1)/(3.5).(1)/(2^(3))+....=

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

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  10. 5x-(13)/(2)x^(2)+(35)/(3)x^(3)-(97)/(4)x^(4)+....=

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

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

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

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

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

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

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

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

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

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