Question

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

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