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The sum of the series Sigma(oo)^(n=0) (n...

The sum of the series `Sigma_(oo)^(n=0) (n^(2)-n+1)/(n!)` is

A

2e

B

`(3)/(2)e`

C

e

D

3e

Text Solution

Verified by Experts

We have
`underset(n=0)overset(infty)Sigma(n^(2)-n+1)/(n!)=underset(n=0)overset(infty)Sigma(n^(2))/(n!)-underset(n=0)overset(infty)Sigma(n)/(n!)+underset(n=0)overset(infty)Sigma(1)/(n!)`
`=2e-e+e=2e ["before" underset(n=0)overset(infty)Sigma=2e and underset(n=0)overset(infty)Sigma (n)/(n!)=e]`
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OBJECTIVE RD SHARMA-EXPONENTIAL AND LOGARITHMIC SERIES-Section I - Solved Mcqs
  1. If y=-{x^(3)+(x^(6))/(2)+(x^(9))/(3)+….} then

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  2. (1)/(n!)+(1)/(2!(n-2)!)+(1)/(4!(n-4)!)+….to n terms is equal to

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  3. The sum of the series Sigma(oo)^(n=0) (n^(2)-n+1)/(n!) is

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  4. (2)/(1!)+(4)/(3!)+(6)/(5!)+….infty is equal to

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  5. The coefficient of x^(10) in the expansion o f10^(x) in ascending powe...

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  6. In the expansion of (e^(x)-1-x)/(x^(2)) is ascending powers of x the f...

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  7. In the expansion of log(10)(1-x),|x|lt1 the coefficient of x^(n) is

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  8. Sum of series 9/(1!)+19/(2!)+35/(3!)+57/(4!)+... (A) 7e-3 (B) 12e-5...

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  9. The constant term in the expansion of (3^(x)-2^(x))/(x^(2)) is

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  10. Sigma(n=1)^(oo) (x^(2n))/(2n-1) is equal to

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  11. Then sum of the series 1+(1|3)/(2!)x+(1|3|5)/(3!)x^(2)+(1+3+5+7)/(4...

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  12. 1/(e^(3x))(e^x+e^(5x))=a0+a1x+a2x^2+........=>2a1+2^3a3+2^5a5+......=

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  13. Let S=x-(x^(3))/(3!)+(x^(5))/(5!)… and C=1-(x^(2))/(2!)+(x^(4))/(4!) T...

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  14. The sum of series 2/(3!)+4/(5!)+6/(7!)+...........oo is :

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  15. The sum of the series S=Sigma(n=1)^(infty)(1)/(n-1)! is

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  16. The sum of the series loge(3)+(loge(3))^3/(3!)+(loge(3))^5/(5!)+....+ ...

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  17. The value of 1+(log(e)x)+(log(e)x)^(2)/(2!)+(log(e)x)^(3)/(3!)+…inft...

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  18. (1+3)loge3+(1+3^2)/(2!)(loge3)^2+(1+3^3)/(3!)(loge 3)^3+....oo= (a)28...

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  19. If agt0 and x in R, then 1+(xlog(e)a)+(x^(2))/(2!)(log(e)a)^(2)+(x^(...

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  20. (2)/(2!)+(2+4)/(3!)+(2+4+6)/(4!)+….infty is equal to

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