Dhaka Secondary 2009/4

Problem for Secondary Group from Divisional Mathematical Olympiad will be solved here.
Forum rules
Please don't post problems (by starting a topic) in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

Dhaka Secondary 2009/4

$( 1-\frac{1}{2^2} ) ( 1- \frac{1}{3^2} ) ( 1- \frac{1}{4^2} ) ( 1- \frac{1}{5^2} ) (1- \frac{1}{6^2} ) \cdots (1- \frac{1}{1000^2} ) =?$

Zzzz
Posts: 172
Joined: Tue Dec 07, 2010 6:28 am
Location: 22° 48' 0" N / 89° 33' 0" E

Re: Dhaka Secondary 2009/4

Nice problem ..
Every logical solution to a problem has its own beauty.

Shifat
Posts: 53
Joined: Sun Jul 31, 2011 12:21 pm
I found a sequence out of the serial multiplications, my result is $\frac{1001}{2000}$