1/3*4+1/4*5+1/5*6+.......+1/49*50用简便计算怎么运用？注意1/3*4其实是1/12，其他的也一样！！！

Question

如题所述

Answer 1

1/3*4+1/4*5+1/5*6+.......+1/49*50
=(1/3-1/4)+(1/4-1/5)+........+(1/48-1/49)+(1/49-1/50)
=1/3-1/50=47/150
记得规律，1/[n*(n+1)]=1/n-1/(n+1)

Answer 2

1/3*4+1/4*5+1/5*6+.......+1/49*50
=1/3-1/4+1/4-1/5+1/5-1/6+……+1/49-1/50
=1/3-1/50
=47/150

Answer 3

记住一个公式：1/n*(n+1)=1/n-1/(n+1)
所以原式变为：1/3-1/4+1/4-1/5………………-1/49+1/49-1/50
＝1/3-1/50=47/150

Answer 4

1/3*4+1/4*5+1/5*6+.......+1/49*50=1/3-1/4+1/4-1/5+......1/49-1/50=1/3-1/50=47/150

Answer 5

楼上已经写出来了嘛