\(\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{2015.2017}\)
\(=\frac{3}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{2015.2017}\right)\)
\(=\frac{3}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(=\frac{3}{2}.\left(1-\frac{1}{2017}\right)\)
\(=\frac{3}{2}.\frac{2016}{2017}\)
\(=\frac{3024}{2017}\)
_Chúc bạn học tốt_
\(\frac{3}{1.3}\)+ \(\frac{3}{3.5}\)+ ... + \(\frac{3}{2015.2017}\) = (3 - 1) : 2 + (1 - \(\frac{3}{5}\)) : 2 + ... + (\(\frac{3}{2015}\)- \(\frac{3}{2017}\)) : 2
= (3 - 1 + 1 -\(\frac{3}{5}\)+ ... + \(\frac{3}{2015}\) - \(\frac{3}{2017}\)) : 2
= (3 - \(\frac{3}{2017}\)) : 2
= \(\frac{6048}{2017}\) : 2
= \(\frac{3024}{2017}\)
\(\frac{3}{1.3}+\frac{3}{3.5}+.....+\frac{3}{2015.2017}\)=\(\frac{3}{2}(\frac{2}{1.3}+\frac{2}{3.5}+.........+\frac{2}{2015.2017})\)
= \(\frac{3}{2}(\frac{3-1}{1.3}+\frac{5-3}{3.5}+...........+\frac{2017-2015}{2015.2017})\) = \(\frac{3}{2}(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{2015}-\frac{1}{2017})\) = \(\frac{3}{2}(1-\frac{1}{2017})=\frac{3}{2}.\frac{2016}{2017}=\frac{3024}{2017}\)
\(A=\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{2015.2017}\)
\(A=\frac{3}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(A=\frac{3}{2}\cdot\left(1-\frac{1}{2017}\right)\)
\(A=\frac{3}{2}\cdot\frac{2016}{2017}\)
\(A=\frac{3024}{2017}\)
