Ta có:\(P=\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+....+\frac{48}{2}+\frac{49}{1}+50-50\)
\(=\left(1+\frac{1}{49}\right)+\left(1+\frac{2}{48}\right)+\left(1+\frac{3}{47}\right)+...+\left(1+\frac{48}{2}\right)+\left(1+\frac{49}{2}\right)-50\)
\(=\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+....+\frac{50}{2}+\frac{50}{1}-50\)
\(=50\left(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+....+\frac{1}{2}\right)+50-50\)
\(=50\left(\frac{1}{49}+\frac{1}{48}+\frac{1}{47}+....+\frac{1}{2}\right)\)
mà \(S=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+....+\frac{1}{49}\)
\(=>\frac{S}{P}=\frac{1}{50}\)
Vậy \(\frac{S}{P}=\frac{1}{50}\)
