1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...1/39*40=???(化简！！)

Question

1 1 1 1 1
___+___+___+___+……+___=???? 急急急急急急！！！！！！！！！！！
1x2 2x3 3x4 4x5 39x40
化简要详细！！！！！

Answer 1

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...1/39*40
=(1-1/2)+(1/2-1/3)+....+(1/39-1/40)
=1-1/40
=39/40

Answer 2

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+...1/39*40
=(1-1/2)+(1/2-1/3)+....+(1/39-1/40)
=1-1/40
=39/40