Possible Duplicate:
Result of the product $0.9 \times 0.99 \times 0.999 \times \dots$
How to find the product $\left(1 - \frac{1}{a}\right)\left(1-\frac{1}{a^{2}}\right)\left(1-\frac{1}{a^{3}}\right)\ldots$ where $a>1$? I tried opening the first few brackets and then then finding some pattern. Is there any shorter way? Thanks.
$PS$- This was a question in my textbook where $a = 5$ but I wanted to know a more general way.