Infinite Product q (1 Viewer)

[milton]

What is the limit (if any) of the infinite product

(1-1/2)(1-1/4)(1-1/8)(1-1/16)(1-1/32)...(1-2^(-n)) as n-->oo ?

It seems to hover around 0.28888, but it might also approach 0 extremely slowly.

 

[darkliight]

It does converge (ie, it's non-zero) but it's not a nice number apparently. Check out equations 49 and 50 at http://mathworld.wolfram.com/InfiniteProduct.html.

As an aside, there are a bunch of convergence tests for infinite products if you ever need. Some (most?) are similar to the infinite series tests.