|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?
1/3-1/2

这样两个相邻数为分母的相乘都等于它们直接拆开的两个数的差.
因此,原式=-1+1/2-1/2+1/3-1/3+1/4-......+1/2005
=-2004/2005