5/1×2+5/2×3+5/3×4+……+5/48×49+5/49×50
=5(1/1×2+1/2×3+1/3×4+……+1/48×49+1/49×50)
=5(1/1-1/2+1/2-1/3+1/3-1/4+……+1/48-1/49+1/49-1/50)
=5(1-1/50)
=5×49/50
=49/10