I need to find the product:
(1-1/2)(1-1/3)(1-1/4)(1-1/5)......(1-1/499)(1-1/500) =
NOTICE: The list goes from (1-1/2) all the way to
(1 - 1/500).
How do I solve this question?
How do I find the product?
Your formula is not correct
$\displaystyle =\frac{(500-1)(500-2).....(2)(1)}{(500)(499)...(2)(1)}$
$\displaystyle =\frac{(500-1)!}{500!}$
$\displaystyle =\frac{(499)!}{500!}$
Remember that (n-1)! is not equal to (1-n)!
$\displaystyle =\frac{(n-1)!}{n!} = \frac{1}{n} {\color{red}\ne} \frac{(1-n)!}{n!}$
$\displaystyle =\frac{1}{500}$