Cho S = \(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) +..................+ \(\frac{1}{48}\) + \(\frac{1}{49}\) + \(\frac{1}{50}\) Và P = \(\frac{1}{49}\) + \(\frac{2}{48}\) + \(\frac{3}{47}\) + ............\(\frac{48}{2}\) + \(\frac{49}{1}\)
Hãy tính \(\frac{S}{P}\)
Giải chi tiết giúp mk nha các bn, mk cảm ơn nhìu ạ!!
Ta có: \(P=\frac{1}{49}+\frac{2}{48}+\frac{3}{47}+...+\frac{48}{2}+\frac{49}{1}\)
\(\Rightarrow P=\left(1+\frac{1}{49}\right)+\left(1+\frac{2}{48}\right)+\left(1+\frac{3}{47}\right)+...+\left(1+\frac{48}{2}\right)+1\)
\(\Rightarrow P=\frac{50}{49}+\frac{50}{48}+\frac{50}{47}+...+\frac{50}{2}+\frac{50}{50}\)
\(\Rightarrow P=50\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}\right)\)
\(\Rightarrow\frac{S}{P}=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}}{50\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{50}\right)}=\frac{1}{50}\)
Vậy \(\frac{S}{P}=\frac{1}{50}\)
