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

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

A

`(2)/(1!)+(4)/(3!)+(6)/(5!)+"......."oo=e`

B

`((2)/(1!)+(4)/(3!)+(6)/(5!)+"......."oo)/((1)/(1!)+(1)/(3!)+(1)/(5!)+"........"oo) = ( e-1)/(e+1)`

C

`2 sum_(n=2)^(oo) ""^(n)C_(2) = ( 3^(n-2))/(n!) = e^(3)`

D

`sum_(n=2)^(oo) (""^(n)C_(2))/((n+1)!) = e-2`

Text Solution

Verified by Experts

The correct Answer is:
D
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