Question

计算：1/2-1的绝对值+1/3-1/2的绝对值+1/4-1/3的绝对值+...+1/2011-1/2010的绝对值+1

Answer 1

|1/2-1|+|1/3-1/2|+|1/4-1/3|+…+|1/2011-1/2010|+|1/2012-1/2011|=1-1/2+1/2-1/3+1/3-1/4+…+1/2010-1/2011+1/2011-1/2012=1-1/2012=2011/2012