Question

Tính \(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{102}}{\frac{101}{1}+\frac{100}{2}+\frac{99}{3}+...+\frac{1}{101}}\)

Answer 1

\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{102}}{\frac{101}{1}+\frac{100}{2}+\frac{99}{3}+...+\frac{1}{101}}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{102}}{\left(\frac{100}{2}+1\right)+\left(\frac{99}{3}+1\right)+...+\left(\frac{1}{101}+1\right)+1}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{102}}{\frac{102}{2}+\frac{102}{3}+...+\frac{102}{101}+\frac{102}{102}}\)

\(A=\frac{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{102}}{102.\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{101}+\frac{1}{102}\right)}\)

\(A=\frac{1}{102}\)

Answer 2

A = 1/102