\(A=\frac{4}{2}+\frac{4}{6}+\frac{4}{12}+\frac{4}{20}+\frac{4}{30}+\frac{4}{42}\)
\(A=\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+\frac{4}{4.5}+\frac{4}{5.6}+\frac{4}{6.7}\)
\(A=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=4\left(1-\frac{1}{7}\right)\)
\(A=4.\frac{6}{7}\)
\(A=\frac{24}{7}\)
\(A=\frac{4}{2}+\frac{4}{6}+\frac{4}{12}+\frac{4}{20}+\frac{4}{30}+\frac{4}{42}=4\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=4\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=4\left(1-\frac{1}{7}\right)=\frac{6}{7}.4=\frac{24}{7}\)
A = \(\frac{4}{2}+\frac{4}{6}+\frac{4}{12}+\frac{4}{20}+\frac{4}{30}+\frac{4}{42}\)
A = \(\frac{4}{2}+\frac{4}{2.3}+\frac{4}{3.4}+\frac{4}{4.5}+\frac{4}{5.6}+\frac{4}{6.7}\)
A x 4 = \(\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)
A x 4 = \(1-\frac{1}{7}\)
A x 4 = \(\frac{6}{7}\)
A = \(\frac{6}{7}:4\)
A = \(\frac{3}{14}\)