Ta có : \(C=\frac{1}{12}+\frac{1}{30}+\frac{1}{56}+...+\frac{1}{2652}=\frac{1}{3.4}+\frac{1}{5.6}+\frac{1}{7.8}+..+\frac{1}{51.52}\)
\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{51}-\frac{1}{52}\)
\(=\left(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{51}+\frac{1}{52}\right)-2\left(\frac{1}{8}+\frac{1}{10}+...+\frac{1}{52}\right)\)
\(=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+...+\frac{1}{51}+\frac{1}{52}-\left(\frac{1}{4}+\frac{1}{5}+...+\frac{1}{26}\right)\)\(=\frac{1}{27}+\frac{1}{28}+...+\frac{1}{52}\)
Khi đó ta không thể chứng minh C < 1/4 vì sở dĩ \(\frac{1}{27}+\frac{1}{28}+...+\frac{1}{34}>\frac{1}{4}\)(bạn thử lấy máy tính tính xem)
