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

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

A

e

B

`n!`

C

`e n!`

D

`e//n!`

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Verified by Experts

The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-EXPONENTIAL SERIES & LOGARITHMIC SERIES (APPENDIX-1)-EXERCISE 1A
  1. The coefficient of x^(5) in the expansion of (1-2x+3x^(2))/(e^(x)) is

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

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

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

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

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

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

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  8. 2-(3^(2))/(2!)+(3^(3))/(3!)-(3^(4))/(4!)+....=

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  9. (1)/(2!)+(1)/(3!)+(1)/(4!)+....=

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  10. (1)/(2!)-(1)/(3!)+(1)/(4!)-(1)/(5!)+....=

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  11. -1+(2^(2))/(2!)-(2^(3))/(3!)+(2^(4))/(4!)-....=

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

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

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  14. underset(n=1)overset(oo)Sigma(1)/((2n-1)!)=

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  15. underset(n=1)overset(oo)Sigma(x^(n))/((2n-1)!)=

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  16. The sum of series (1)/(2!)+(1)/(4!)+(1)/(6!)+... is

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  17. 1+(1)/(3!)+(1)/(5!)+....=

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  18. (2)/(1!)+(4)/(3!)+(6)/(5!)+....=

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  19. (3)/(2!)+(5)/(4!)+(7)/(6!)+(9)/(8!)+....=

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  20. 2[1+((log(e)a)^(2))/(2!)+((log(e)a)^(4))/(4!)+....]=

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