Convergence of Infinite Series with Increasing Denominators

[pixel01]

S=1/2+1/(2*4)+1/(2*4*6)...+1/(2*4*6..2n)+...

I want to calculate the sum of this series, but it seems not to converge.
Can anyone help me

Thank you.

 

[matt grime]

It does converge, the sum is$$\sum_{n=1}^{\infty} \frac{1}{n!2^n}$$

which is a well known series (what Taylor series do you know?).

 

[pixel01]

Thank you, yes it does converge. Could you please tell me how to calculate the sum.
I should revise some old maths books.

 

[morphism]

He did tell you how to calculate the sum:

which is a well known series (what Taylor series do you know?).

 

[pixel01]

I found it myself. The Taylor expansion of e^x at 1/2. Thanks.