Question

If C is coefficient of x^2 in the equation (1-x)(1+2x)(1-3x)(1+4x)...(1+14x)(1-15x) , fine the value of |C|

Answer 1

|C| is the sum of the products of the numbers 1, 2,....,15 taken fourteen at a time. So |C| = 15!/1 + 15!/2 +...+ 15!/14 = 15![1/1 + 1/2 +...+1/14] = 4.251984 x 10¹²