# Does this series converge

1. Oct 17, 2007

### 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.

2. Oct 17, 2007

### 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?).

3. Oct 17, 2007

### pixel01

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

4. Oct 17, 2007

### morphism

He did tell you how to calculate the sum:

5. Oct 19, 2007

### pixel01

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