Question

x/3+x/15+x/35+⋯+x/(2015*2017)=2016/2017
unde / este linie de fractie

Answer 1

[tex]\frac{x}{3}+\frac{x}{15}+\frac{x}{35}+...+\frac{x}{2015\cdot2017}=\frac{2016}{2017}\\ \frac{x}{2}(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{2015\cdot2017})=\frac{2016}{2017}\\ \frac{x}{2}(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2015}-\frac{1}{2017})=\frac{2016}{2017}\\ \frac{x}{2}(1-\frac{1}{2017})=\frac{2016}{2017}\\ \frac{x}{2}\cdot \frac{2016}{2017}=\frac{2016}{2017}\\ \frac{x}{2}=1\Rightarrow \boxed{\boxed{x=2}} [/tex]