1/1×5+1/5×10+1/10×15……1/45×50=有什么规律?

1/1×5+1/5×10+1/10×15……1/45×50=
有什么规律?

1/1×5+1/5×10+1/10×15……1/45×50
=1/5+1/5*(1/5-1/10)+1/5*(1/10-1/15)+...+1/5*(1/45-1/50)
=1/5+1/5*(1/5-1/10+1/10-1/15+...+1/45-1/50)
=1/5+1/5*(1/5-1/50)
=1/5+1/5*9/50
=1/5*(1+9/50)
=1/5*59/50
=59/250
希望对您有所帮助