It is known that / XY - 2 / (this is the sign of absolute value) and / Y - 1 / are opposite numbers (1) Find the value of X and y; (2) Find 1 / (this is the fractional sign) XY + 1 / (x + 1) (y + 1) + 1 / (x + 2) (y + 2) +... + 1 / (x + 2009) (y + 2009)

It is known that / XY - 2 / (this is the sign of absolute value) and / Y - 1 / are opposite numbers (1) Find the value of X and y; (2) Find 1 / (this is the fractional sign) XY + 1 / (x + 1) (y + 1) + 1 / (x + 2) (y + 2) +... + 1 / (x + 2009) (y + 2009)

1: Absolute value is always greater than or equal to 0 | XY-2 | + | Y-1 | = 0 | XY-2 | = 0, | Y-1 | = 0xy = 2y-1 = 0y = 1, x = 22:1 / XY + 1 / (x + 1) (y + 1) +... + 1 / (x + 2009) (y + 2009) = 1 / 2 * 1 + 1 / 3 * 2 + 1 / 4 * 3 +... + 1 / 2011 * 2010 = 1-1 / 2 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 +... + 1 / 2010-1 / 2011 = 1-1 / 2011 = 2010 / 2