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