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If a=sum(n=1)^(oo)((2n))/(2n-1),b sum(n=...

If `a=sum_(n=1)^(oo)((2n))/(2n-1),b sum_(n=1)^(oo) (2n)/(2n+1!)` then ab =

A

1

B

`e^2`

C

`(e-1)/(e+1)`

D

`(e+1)/(e-1)`

Text Solution

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The correct Answer is:
A
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AAKASH SERIES-EXPONENTIAL SERIES -EXERCISE - II (A) (CLASS WORK)
  1. Assertion (A) : x + x^(2)/(1!) + x^(3) /(2!) + (x^4)/(3!) + .....+ oo ...

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  2. (a+b).(a-b)+((a+b)(a-b)(a^2+b^2))/(2!)+((a+b)(a-b)(a^4+b^4+a^2b^2))/(3...

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  3. If a=sum(n=1)^(oo)((2n))/(2n-1),b sum(n=1)^(oo) (2n)/(2n+1!) then ab =

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  4. P = 1 - (3)/(1!) + 9/(2!) - (27)/(3!) + ....... Q = 1+ (4)/(1!) +(16...

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  5. If y = sum(n=2)^(oo) (""^nc2 .(3^(n-2))/(n!)) then 2y =

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  6. x +(x^2)/(3!)+(x^3)/(5!) + ......oo =

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  7. sum(n=0)^(oo)((loge x)^(2n))/((2n)!)=

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  8. (1+x^2/(2!) +x^4 /(4!) + .....oo)^(2) - (x+x^3/(3!) +x^(5)/(5!) + .......

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  9. 1 +1(4.2!) + 1/(16.4!) +1/(64.6!) + ....... =

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  10. 4/(1!) +16/(3!)+(64)/(5!) + ......=

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  11. (1+(2^2)/(2!)+(2^4)/(3!)+(2^6)/(4!)+.....oo)/(1+(1)/(2!)+(2)/(3!)+(2^2...

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  12. 1 + (1+2)/(2!) + (1+2+3)/(3!) + (1+2+3+4)/(4!) + ......oo

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  13. 1+ 1/(2!)+2/(3!)+4/(2!)+ .... oo =

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  14. (1.3)/(1!) +(2.4)/(2!)+(3.5)/(3!) + (4.6)/(4!) + .......oo = .......

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  15. (1^(2).2^2)/(1!) +(2^(2).3^2)/(2!) + (3^(2).4^2)/(3!) + .....oo =

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  16. Assertion (A) : The value of (2)/(1!) +6/(2!)+(12)/(3!) +(20)/(4!) + ....

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  17. Which of the following statement is true Statement - I Coefficient o...

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  18. sum(n=1)^(oo) n^2/((n+1))

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  19. sum(n=1)^(oo)(2 n^2+n+1)/((n!)) =

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  20. sum(n=1)^(oo) 1/(k!) (sum(n=1)^(k)2^(n-1))=

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