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The sum of the series 1+(1^2+2^2)/(2!)...

The sum of the series
`1+(1^2+2^2)/(2!)+(1^(2)+2^(2)+3^(2))/(3!)+(1^(2)+2^(2)+3^(2)+4^2)/(4!)`+.. Is

A

3e

B

`(17)/(6)e`

C

`(31)/(6)e`

D

`(13)/(6)e`

Text Solution

Verified by Experts

The correct Answer is:
c
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OBJECTIVE RD SHARMA-EXPONENTIAL AND LOGARITHMIC SERIES-Exercise
  1. If alpha,beta are the roots of the equation ax^(2)+bx+c=0 then log(a-b...

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  2. The sum of the series 1+(1+2)/(2!)+(1+2+2^(2))/(3!)+(1+2+2^(2)+2^(3)...

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  3. The sum of the series 1+(1^2+2^2)/(2!)+(1^(2)+2^(2)+3^(2))/(3!)+(1^(...

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  4. The coefficent of x^(n) in the series 1+(a+bx)/(1!)+(a+bx)^(2)/(2!)+...

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  5. The sum of the series (1^(2).2^(2))/(1!)+(2^(2).3^(2))/(2!)+(3^(2).4^(...

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  6. The value of (x+y)(x-y)+1/(2!)(x+y)(x-y)(x^2+y^2)+1/(3!)(x+y)(x-y)(x^4...

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  7. If e^(x)=y+sqrt(1+y^(2) then the value of y is

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  8. If (e^(5x)+e^(x))/(e^(3x)) is expand in a series of ascending powers o...

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  9. In the expansion of (e^(7x)+e^(3x))/(e^(5x)) the constant term is

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  10. The value of sqrt(2-1)/sqrt(2)+3-2sqrt(2)/(4)+5sqrt(2-7)/6sqrt(2)+17-1...

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  11. If y=2x^(2)-1 then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…infty equals...

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  12. If S=Sigma(n=2)^(oo) ""^(n)C(2) (3^(n-2))/(n!) then S equals

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  13. If (e^(x))/(1-x) = B(0) +B(1)x+B(2)x^(2)+...+B(n)x^(n)+... , then the ...

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  14. IfS=Sigma(n=1)^(oo) (""^(n)C(0)+""^(n)C(1)+""^(n)c(2)+..+""^(n)C(n))/(...

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  15. If S=Sigma(n=2)^(oo) (""^(n)C(2))/(n+1)! then S equals

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  16. 1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

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  17. The sum of the series (12)/(2!)+(28)/(3!)+(50)/(4!)+(78)/(5!)+…is

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  18. If a=sum(n=0)^(oo) (x^(3n))/((3n)!) , b=sum(n=1)^(oo) (x^(3n-2))/((3n-...

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  19. If S(n) denotes the sum of the products of the products of the first n...

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  20. Sigma(n=0)^(oo) (log(e)x)^(n)/(n!) is equals to

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