\(A=\dfrac{1}{19}+\dfrac{1}{19.29}+\dfrac{1}{29.39}+....+\dfrac{1}{1999.2009}\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}.\left(\dfrac{10}{19.29}+\dfrac{10}{29.39}+.....+\dfrac{10}{1999.2009}\right)\)
\(A=\dfrac{1}{19}+\dfrac{9}{10}.\left(\dfrac{1}{19}-\dfrac{1}{2009}\right)=\dfrac{1}{19}+\dfrac{9}{10}.\dfrac{1}{19}-\dfrac{9}{10}.\dfrac{1}{2009}\)
\(A=\dfrac{1}{19}.\dfrac{19}{10}-\dfrac{9}{10}.\dfrac{1}{2009}\)
\(A=\dfrac{1}{10}-\dfrac{9}{20090}=\dfrac{200}{2009}\)
Vì là các giá trị đại lượng tỉ lệ thuận nên :
\(\dfrac{y_1}{x_1}=\dfrac{y_2}{x_2}=k\)
Áp dụng tính chất dãy tỉ số bằng nhau , ta có :
\(\dfrac{y_1}{x_1}=\dfrac{y_2}{x_2}=\dfrac{y_1-y_2}{x_1-x_2}=\dfrac{10}{6+9}=\dfrac{2}{3}\)
\(\Rightarrow\left\{{}\begin{matrix}y_1=4\\y_2=6\end{matrix}\right.\Rightarrow y_1+y_2=10\)