Question

`P=(C_2^1*C_4^2*C_6^3*...*C_2014^1007)/(C_1^1*C_3^2*C_5^3*...*C_2013^1007)` What is the value of P?

Answer 1

`2^1007`

Explanation:

We have

`p_k = (((2k),(k)))/(((2k-1),(k))) = 2` then

`prod_(k=1)^1007 p_k = 2^1007`