Question

Cho 50.A=\(\frac{49}{1}+\frac{48}{2}+\frac{47}{3}+...+\frac{2}{48}+\frac{1}{49}\)

Answer 1

\(50\cdot A=\frac{49}{1}+\frac{48}{2}+\frac{47}{3}+...+\frac{2}{48}+\frac{1}{49}\)

\(50\cdot A=1+\left(\frac{48}{2}+1\right)+\left(\frac{47}{3}+1\right)+...+\left(\frac{2}{48}+1\right)+\left(\frac{1}{49}+1\right)\)

\(50\cdot A=\frac{50}{50}+\frac{50}{2}+\frac{50}{3}+...+\frac{50}{48}+\frac{50}{49}\)

\(50\cdot A=50\cdot\left(\frac{1}{50}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{48}+\frac{1}{49}\right)\)

\(\Rightarrow A=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{48}+\frac{1}{49}+\frac{1}{50}\)