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The coefficient of x^(n) in the expansio...

The coefficient of `x^(n)` in the expansion of `(1)/(x^(2)-5x+6)"for"|x|lt1` is

A

`1/(2^(n-1))-1/(3^(n-1))`

B

`1/(2^(n+2))-1/(3^(n+2))`

C

`1/(2^(n+1))-1/(3^(n-1))`

D

`1/2^(n)-1/3^(n)`

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-PARTIAL FRACTIONS-EXERCISE 1
  1. (2x-3)/((x-1)(x^(2)+1)^(2))=

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  2. If (1)/((ax+b)(cx+d))=(A)/(ax+b)+(B)/(cx+d) then (1)/((ax+b)^(2)(cx+d)...

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  3. If (1)/((x-a)(x^(2)+b))=(A)/(x-a)+(Bx+C)/(x^(2)+b) then (1)/((x-a)(x^(...

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  4. To find the coefficient of x^(4) in the expansion of (3x)/((x-2)(x-1))...

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  5. The coefficient of x^(3) " in " (5x+6)/((2+x)(1-x)) is

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  6. If abs(x) lt 1 then the coefficient of x^(2) in the expansion of (3x)/...

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  7. The coefficient of x^(n) in the expansion of (1)/(x^(2)-5x+6)"for"|x|l...

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  8. The coefficient of x^(n) in (x-4)/(x^(2)-5x+6) is

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  9. If (x-4)/(x^(2)-5x+6) can be expanded in the ascending powers of x, th...

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  10. The coefficient of x^(n) " in " x/((x-a)(x-b)) is

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  11. The coefficient of x^(n) in (1)/((1-2x)(1-3x)) is

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  12. For |x| lt 1/5, the coefficient of x^(3) in the expansion of (1)/((1-...

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  13. If the expansion in powers of x of the function (1)/((1-ax)(1-bx)) is ...

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  14. The coefficient of x^(n) " in " 1/((1-x)(1-2x)(1-3x)) is

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  15. The coefficient of x^(n) " in " ((1+x)(1-2x)(1-3x))/((1-x)(1-2x)(1-3x)...

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  16. The coefficient of x^(n) in (x+1)/((x-1)^(2)(x-2)) is

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  17. The coefficient of x^(n) in (x+1)/((x-1)^(2)(x-2)) is

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  18. For |x| lt 1, the constant term in the expansion of (1)/((x-1)^(2)(x-2...

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  19. The coefficient of x^(5) " in " (x^(2)+1)/((x^(2)+4)(x-2)) is

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  20. The coefficient of x^(4) " in " (3x^(2)+2x)/((x^(2)+2)(x-3)) is

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