小学计算题五年级

=1-1/2+1/2-1/3+1/3-........+1/49-1/50
=1-1/50
=49/50

这题主要是要你明白1/2*3=1/2-1/3 1/3*4=1/3-1/4(裂顶法)
看楼主心情给分啦。。。

1/(1*2)+1/(2*3)+1/(3*4)+……+1/(49*50)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/49-1/50)
=1-1/50
=49/50

俗称：裂顶法（即分解因子）

1/(1*2)+1/(2*3)+1/(3*4)+……+1/(49*50)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/49-1/50)
=1-1/50
=49/50

49/50