Question

tim x: 1/5 x 7+1/7x9+...+1/X(x+2)=7/95

Answer 1

Đặt VT=A

\(2A=\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{x\left(x+2\right)}\)

\(2A=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+2}\)

\(A=\left(\frac{1}{5}-\frac{1}{x+2}\right):2\)

Thay A vào VT ta đc:

\(\left(\frac{1}{5}-\frac{1}{x+2}\right):2=\frac{7}{95}\)

\(\frac{1}{5}-\frac{1}{x+2}=\frac{14}{95}\)

\(\frac{1}{x+2}=\frac{1}{19}\)

\(\Rightarrow x+2=19\)

\(\Rightarrow x=17\)

Answer 2

\(\text{Đặt VT=A }\)

\(2A=\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{x\left(x+2\right)}\)

\(2A=\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+2}\)

\(A=\left(\frac{1}{5}-\frac{1}{x+2}\right):2\)

\(\text{Thay A vào VT ta đc: }\)

\(\left(\frac{1}{5}-\frac{1}{x+2}\right):2=\frac{7}{95}\)

\(\frac{1}{5}-\frac{1}{x+2}=\frac{14}{95}\)

\(\frac{1}{x+2}=\frac{1}{19}\)

\(\Rightarrow x+2=19\)

\(\Rightarrow x=17\)