\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\)
\(=1-\frac{1}{7}\)
\(=\frac{6}{7}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)
\(=\frac{1}{1}X2+\frac{1}{2}X3+\frac{1}{3}X4+\frac{1}{4}X5+\frac{1}{5}X6+\frac{1}{6}X7\)
\(=\) \(\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+\left(\frac{1}{4}-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{6}\right)+\left(\frac{1}{6}-\frac{1}{7}\right)\)
\(=1-\frac{1}{7}\)
\(=\frac{6}{7}\)
Bạn xem lời giải của mình nhé:
Giải:
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{42}\\ =\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}\\ =1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)
\(=1-\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+...+\left(\frac{1}{6}-\frac{1}{6}\right)-\frac{1}{7}\\ =1-\frac{1}{7}\\ =\frac{7-1}{7}\\ =\frac{6}{7}\)
Chúc bạn học tốt!
Đặt A=\(\frac{1}{2}\)+\(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{20}\)+\(\frac{1}{30}\)+\(\frac{1}{42}\)
A=\(\frac{1}{1\cdot2}\)+\(\frac{1}{2\cdot3}\)+\(\frac{1}{3\cdot4}\)+\(\frac{1}{4\cdot5}\)+\(\frac{1}{5\cdot6}\)+\(\frac{1}{6\cdot7}\)
A=\(\frac{2-1}{1\cdot2}\)+\(\frac{3-2}{2\cdot3}\)+\(\frac{4-3}{3\cdot4}\)+\(\frac{5-4}{4\cdot5}\)+\(\frac{6-5}{5\cdot6}\)+\(\frac{7-6}{6\cdot7}\)
A=\(\frac{2}{1\cdot2}\)-\(\frac{1}{1\cdot2}\)+\(\frac{3}{2\cdot3}\)-\(\frac{2}{2\cdot3}\)+\(\frac{4}{3\cdot4}\)-\(\frac{3}{3\cdot4}\)+\(\frac{5}{4\cdot5}\)-\(\frac{4}{4\cdot5}\)+\(\frac{6}{5\cdot6}\)-\(\frac{5}{5\cdot6}\)+\(\frac{7}{6\cdot7}\)-\(\frac{6}{6\cdot7}\)
A=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{6}\)+\(\frac{1}{6}\)-\(\frac{1}{7}\)(rút gọn)
A=1-\(\frac{1}{7}\)
A=\(\frac{6}{7}\)
