Question

1/1*2+1/2*3+1/3*4+......+1/49*50=?

简便计算啊

Answer 1

1/1*2=1-1/2
1/2*3=1/2-1/3
……
1/49*50=1/49-1/50

所以原式=1-1/2+1/2-1/3……+1/49-1/50=1-1/50=49/50

叫裂项法

Answer 2

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