\(A=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{16}\)
\(\Leftrightarrow A=\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{16}\right)+\left(\frac{1}{3}+\frac{1}{5}+...+\frac{1}{15}\right)\)
Đặt \(\frac{1}{2}+\frac{1}{4}+...\frac{1}{16}=B\)
\(\Rightarrow2B=1+\frac{1}{2}+\frac{1}{3}...+\frac{1}{8}\)
\(2B-B=B=1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}\)
Ta có:
\(A=1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{15}\)
\(A=\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}\right).2+1+\frac{1}{9}+\frac{1}{11}+...+\frac{1}{15}\)
Tính A ra rồi chứng minh nó không phải phân số.