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Find the following sum : (1)/(n!) + (1...

Find the following sum :
`(1)/(n!) + (1)/(2!(n-2)!) + (1)/(4!(n-4)!)+"...."`.

A

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

B

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

C

`(2^(n))/(n!)`

D

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

Text Solution

Verified by Experts

We have
`(1)n!+(1)/(2!(n-2)!)+(1)/(4!(n-4)!)`+…
`=(1)/(n!){(1+.^(n)C_(2)+.^(n)C_(4)+…}`
`=(1)/(n!){.^(n)C_(0)+.^(n)C_(2)+.^(n)C_(4)+…}=(1)/(n!)(2^(n-1))=(2^(n-1))/(n!)`
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OBJECTIVE RD SHARMA ENGLISH-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. Find the following sum : (1)/(n!) + (1)/(2!(n-2)!) + (1)/(4!(n-4)!)+...

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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. The sum of the series (2)/(1!) + (4)/(3!) + (6)/(5!) + ……. "to" oo ...

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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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