(200+1)(200-2)(200+3)(200-4)...(200+2007)(200-2008)=

Решите задачу:

$(200 + 1)(200 - 2)(200 + 3)(200 - 4)...(200+2007)(200 - 2008) =\\\\ \prod\limits_{n = 1}^{2008} \ (200 + (-1)^{n-1}n)\\\\\\ a_1 = 200 + (-1)^{0}*1 = 200 -1\\\\...\\\\ a_{200} = 200 + (-1)^{199}*200 = 200 - 200 = 0\\\\\ ...\\\\ a_{2008} = 200 + (-1)^{2007}*2008 = 200 - 2008\\\\\\ \prod\limits_{n = 1}^{2008} \ 200 + (-1)^{n-1}n = a_1*a_2*...*a_{200}*...*a_{2008} =\\\\ a_1*a_2*...*0*...*a_{2008} = 0$