How prove this $e=\frac{2}{1}\left(\frac{4}{3}\right)^{\frac{1}{2}}\left(\frac{6\cdot 8}{5\cdot 7}\right)^{\frac{1}{4}}\cdots$ I  see this nice equation:
$$e=\dfrac{2}{1}\left(\dfrac{4}{3}\right)^{\frac{1}{2}}\left(\dfrac{6\cdot 8}{5\cdot 7}\right)^{\frac{1}{4}}\left(\dfrac{10\cdot 12\cdot 14\cdot 16}{9\cdot 11\cdot 13\cdot 15}\right)^{\frac{1}{8}}\cdots$$
and this equation who first found it? and   How prove it.
Thank you very much!

This (PDF) has the proof of your equation.
New Wallis- and Catalan-Type Infinite Products for $\pi,e$, and $\sqrt{2+\sqrt 2}$ 
by Jonathan Sondow and Huang Yi
