Which function grows faster?

**Dragonfall** · Jun24-09, 09:21 PM

or

$LaTeX Code: \\prod_{r=0}^{n-1}\\left(\\begin{array}{c}\\sum_{j\\leq r}\\left(\\begin{array}{c}n\\\\ j\\end{array}\\right)\\\\2^r\\end{array}\\right)$

Asymptotically, I mean.

**CRGreathouse** · Jun25-09, 01:37 AM

Since
$LaTeX Code: \\prod_{r=0}^{n-1}{{\\sum_{j<r}{n\\choose j}}\\choose{2^r}}={0\\choose1}\\prod_{r=1}^{n-1}{{\\sum_{j<r}{n\\choose j}}\\choose{2^r}}=0$
I'd have to go with

.

**Dragonfall** · Jun25-09, 01:58 AM

How about now?

**CRGreathouse** · Jun25-09, 03:39 AM

It seems that the product grows faster.