Question

[Jenny phạm]

Tìm x biết :

a) x + \(\frac{4}{5.9}\) +\(\frac{4}{9.13}\) +\(\frac{4}{13.17}\)+ . . . + \(\frac{4}{41.45}\) = −\(-\frac{37}{45}\)

b) \(\frac{5}{1.6}\) +\(\frac{5}{6.11}\) + . . . + \(\frac{5}{\text{(5x+1).(5x+6)}}\) =\(\frac{2015}{2016}\)

c) \(\frac{2}{1.3}\)+\(\frac{2}{3.5}\) +\(\frac{2}{5.7}\) +. . . + \(\frac{2}{x\left(x+2\right)}\) = \(\frac{2017}{2018}\)

Answer 1

[Nguyễn Thị Ngọc Ánh]

\(a,x+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}=--\frac{37}{45}.\)

\(x+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}=\frac{37}{45}\)

\(x+\frac{1}{5}-\frac{1}{45}=\frac{37}{45}\)

\(x+\frac{1}{5}=\frac{37}{45}+\frac{1}{45}=\frac{38}{45}\)

\(x=\frac{38}{45}-\frac{1}{5}=\frac{29}{45}\)

\(b,\frac{5}{1.6}+\frac{5}{6.11}+...+\frac{5}{\left(5x+1\right)\left(5x+6\right)}=\frac{2015}{2016}\)

\(\Rightarrow1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{5x+1}-\frac{1}{5x+6}=\frac{2015}{2016}\)

\(\Rightarrow1-\frac{1}{5x+6}=\frac{2015}{2016}\)

\(\Rightarrow\frac{1}{5x+6}=1-\frac{2015}{2016}=\frac{1}{2016}\)

\(\Rightarrow5x+6=2016\)

\(\Rightarrow5x=2010\Rightarrow x=402\)

\(c,\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{x\left(x+2\right)}=\frac{2017}{2018}\)

\(\Rightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{x}-\frac{1}{x+2}=\frac{2017}{2018}\)

\(\Rightarrow1-\frac{1}{x+2}=\frac{2017}{2018}\)

\(\Rightarrow\frac{1}{x+2}=1-\frac{2017}{2018}=\frac{1}{2018}\)

\(\Rightarrow x+2=2018\Rightarrow x=2016\)

học tốt ~~~