1/50*51+1/51*52+.+1/99*100

问题描述:

1/50*51+1/51*52+.+1/99*100

1/50-1/51+//51-1/52+......+1/99-1/100=1/50-1/100=1/100

原式=1/50-1/51+1/51+......-1/100
=1/100

1/50*51+1/51*52+.+1/99*100
=(1/50-1/51)+(1/511-1/52)+.+(1/99-1/100)
=1/50-1/100
=1/100

1/100