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Infinite limit of factorial series

  1. Jul 5, 2011 #1
    1. The problem statement, all variables and given/known data
    MSP5419g73d00047g3g1200002bha5g9gah09ab35.gif

    3. The attempt at a solution

    I have no idea where to start from.
    I know that e = 1/0! + 1/1! + 1/2! + 1/3! + .......... + 1/n! + .....
    and tried to separate the factorial off the geometric series but had no success.
     
  2. jcsd
  3. Jul 5, 2011 #2
    We start from [tex]\frac{2^{k-1}(k-1)}{(k+1)!} =\frac{2^{k-1}(k+1-2)}{(k+1)!} =
    \frac{2^{k-1}}{k!}-\frac{2^k}{(k+1)!}[/tex] and we recognize a telescopic series.
     
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