\(\frac{3}{2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{17.18}\)
\(=\frac{3.1}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{17.18}\)
\(=3.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{17.18}\right)\)
\(=3.\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{17}-\frac{1}{18}\right)\)
\(=3.\left(1-\frac{1}{18}\right)\)
\(=3.\frac{17}{18}\)
\(=\frac{17}{6}\)
đặt A =\(\frac{3}{2}\)+\(\frac{3}{3x4}\)+...........+\(\frac{3}{17x18}\)
nhân cả 2 vế với \(\frac{1}{3}\)
A x \(\frac{1}{3}\)= \(\frac{1}{2}\)+\(\frac{1}{3x4}\)+..........+\(\frac{1}{17x18}\)
A x \(\frac{1}{3}\) =\(\frac{1}{2}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+...........+\(\frac{1}{17}\)-\(\frac{1}{18}\)
A x \(\frac{1}{3}\)=\(\frac{1}{2}\)+\(\frac{1}{3}\)-\(\frac{1}{18}\)
A x \(\frac{1}{3}\)=\(\frac{7}{9}\)
A = \(\frac{7}{9}\):\(\frac{1}{3}\)
A= \(\frac{7}{3}\)
