\(A=\frac{1}{1.4}+\frac{1}{2.7}+...+\frac{1}{67.70}\)
\(3A=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{67.70}\)
\(3A=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{67}-\frac{1}{70}\)
\(3A=1-\frac{1}{70}=\frac{69}{70}\)
\(A=\frac{69}{70}:3=\frac{23}{70}\)
vì \(\frac{23}{70}< 1\)
nên \(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{67.70}< 1\)
\(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{67.70}\)
\(=3.\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{67.70}\right)\)
\(=\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{67.70}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{67}-\frac{1}{70}\)
\(=1-\frac{1}{70}\)
\(=\frac{69}{70}< 1\)
