If n satisfies the square of (n-2006) + the square of (2008-n) = 1, then (n-2006) (2008-n) is equal to?

If n satisfies the square of (n-2006) + the square of (2008-n) = 1, then (n-2006) (2008-n) is equal to?


Square of (n-2006) + square of (2008-n)
=Square of (n-2006) + square of (2008-n) + 2 (n-2006) (2008-n) - 2 (n-2006) (2008-n)
=(n-2006+2008-n)²-2(n-2006)(2008-n)
=4-2(n-2006)(2008-n)
=1
(n-2006)(2008-n)=(4-1)/2=3/2



(1/1+2)+(1/1+2+3)+…… +(1/1+2+3+4+…… +What is the equivalent of 2008?


The general term formula is 2 / (n + 1) (n + 2), so the sum is 2 (1 / 2-1 / N + 2), that is 1-2 / N + 2