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

The coefficient of `x^(n)` in the expansion of `(e^(7x)+e^(x))/(e^(3x))` is

A

`(4^(n))/(n!)-((-1)^(n)2^(n))/(n!)`

B

`((-1)^(n))/(n!)+((-1)^(n-1)a)/((n-1)!)+((-1)^(n-2))/((n-2)!)`

C

`(4^(n))/(n!)+((-1)^(n)2^(n))/(n!)`

D

`((-1)^(n))/(n!)-((-1)^(n-1)a)/((n-1)!)+((-1)^(n-2))/((n-2)!)`

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 1A
  1. The coefficent of x^(n) in the expansion of (1-x)e^(x) is

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  2. (1)/(e^(3x))(e^(x)+e^(5x))=a(0)+a(1)x+a(2)x^(2)+....implies2a(1)+2^(3)...

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  3. The coefficient of x^(n) in the expansion of (e^(7x)+e^(x))/(e^(3x)) i...

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  4. The coefficient of x^(n) in the expansion of (1+ax+x^(2))/(e^(x)) is

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

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  6. Coefficicent of x^(10) in the expansion of (2+3x)e^(-x) is

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  7. The coefficient of x^(n) in (1-2x)/(e^(x)) is

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  8. The coefficient of x^(5) in the expansion of (1-2x+3x^(2))/(e^(x)) is

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  9. The coefficient of x^(k) in the expansion of (1-2x-x^(2))/(e^(-x)) is

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  10. The coefficient of x^(n) in (1+x)/(1!)+((1+x)^(2))/(2!)+((1+x)^(3))/(3...

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  11. The coefficient of x^(n) in 1+(ax+b)+((ax+b)^(2))/(2!)+((ax+b)^(3))/(3...

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  12. The coefficient of x^(n) in the expansion of underset(n=1)overset(oo)S...

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  13. If n is odd, coefficient of x^(n) in the expansion of (1+(x^(2))/(2!)+...

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  14. If n is even, coefficient of x^(n) in the expansion of (1+(x^(2))/(2!)...

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  15. 2-(3^(2))/(2!)+(3^(3))/(3!)-(3^(4))/(4!)+....=

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  16. (1)/(2!)+(1)/(3!)+(1)/(4!)+....=

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  17. (1)/(2!)-(1)/(3!)+(1)/(4!)-(1)/(5!)+....=

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  18. -1+(2^(2))/(2!)-(2^(3))/(3!)+(2^(4))/(4!)-....=

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  19. Sum of the series 1+(3^(2))/(2!)+(3^(4))/(4!)+(3^(6))/(6!)+...."to "oo...

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  20. underset(n=0)overset(oo)Sigma(1)/((n+1)!)=

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