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If S(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)...

If `S_(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))/(n!)` then
`lim_(n rarr infty) S_(n)` is equal to

A

3e

B

5e

C

7e

D

9e

Text Solution

Verified by Experts

The correct Answer is:
c
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OBJECTIVE RD SHARMA-EXPONENTIAL AND LOGARITHMIC SERIES-Exercise
  1. If y=2x^(2)-1 then (1)/(x^(2))+(1)/(2x^(4))+(1)/(3x^(6))+…infty equals...

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

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

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

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

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  6. 1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

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

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

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

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

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  11. If a = Sigma(n=1)^(oo) (2n)/(2n-1!),b=Sigma(n=1)^(oo) (2n)/(2n+1!) the...

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  12. The value of (1+(a^(2)x^(2))/(2!)+(a^(4)x^(4))/(4!)+…)^(2)-(ax+(a^(3...

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  13. If S(n)=(1^(2).(2))/(1!)+(2^(2).3)/(2!)+(3^(2).4)/(3!)+…(n^(2).(n+1))...

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  14. If S=Sigma(n=0)^(oo) (logx)^(2n)/(2n!) , then S equals

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  15. If y+(y^(3))/(3)+(Y^(5))/(5)+…infty=2(x+(x^(3))/(3)+(x^(5))/(5)+..inft...

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  16. The value of log 2+2 (1/5+1/3.(1)/(5^(3))+1/5.(1)/(5^(5))+..+infty) is

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  17. The sum of the series 1/1.2-1/2.3+1/3.4-1/4.5+ ... is

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  18. e^{(x-1)-1/2(x-1)^2+((x-1)^3)/3-(x-1)^(4)/4+......} is eqaul to

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  19. 2{(m-n)/(m+n)+1/3((m-n)/(m+n))^(3)+1/5((m-n)/(m+n))^(5)+..} is equals ...

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  20. log4 2-log8 2+log16 2-.....oo

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