Question

Tính hợp lí 

6/1.4.7+6/4.7.10+....+6/54.57.60

Answer 1

\(\frac{6}{1.4.7}+\frac{6}{4.7.10}+...+\frac{6}{54.57.60}\)

\(=3.\left(\frac{1}{1.4}-\frac{1}{4.7}\right)+3.\left(\frac{1}{4.7}-\frac{1}{7.10}\right)+...+3.\left(\frac{1}{54.57}-\frac{1}{57.60}\right)\)

\(=3\left(\frac{1}{1.4}-\frac{1}{4.7}+\frac{1}{4.7}-\frac{1}{7.10}+...-\frac{1}{54.57}+\frac{1}{54.57}-\frac{1}{57.60}\right)\)

\(=3\left(\frac{1}{1.4}-\frac{1}{57.60}\right)\)

\(=3\left(\frac{1}{4}-\frac{1}{3420}\right)\)

\(=3\left(\frac{855}{3420}-\frac{1}{3420}\right)\)

\(=3.\frac{427}{1710}\)

\(=\frac{427}{570}\)