BT 7 :
\(P=\frac{12}{1.4.7}+\frac{12}{4.7.10}+\frac{12}{7.10.13}+...+\frac{12}{54.57.60}\)
\(P=\frac{12}{6}\left(\frac{6}{1.4.7}+\frac{6}{4.7.10}+\frac{6}{7.10.13}+...+\frac{6}{54.57.60}\right)\)
\(P=2\left(\frac{1}{1.4}-\frac{1}{4.7}+\frac{1}{4.7}-\frac{1}{7.10}+\frac{1}{7.10}-\frac{1}{10.13}+...+\frac{1}{54.57}-\frac{1}{57.60}\right)\)
\(P=2\left(\frac{1}{1.4}-\frac{1}{57.60}\right)\)
\(P=2\left(\frac{1}{4}-\frac{1}{3420}\right)\)
\(P=\frac{1}{2}-\frac{1}{1710}< \frac{1}{2}\)
Vậy \(P< \frac{1}{2}\)
Chúc bạn học tốt ~