\(A=\frac{5}{2.4.6}+\frac{5}{4.6.8}+...+\frac{5}{16.18.20}\)
\(4A=5.\left(\frac{4}{2.4.6}+\frac{4}{4.6.8}+...+\frac{4}{16.18.20}\right)\)
\(4A=5.\left(\frac{1}{2.4}-\frac{1}{4.6}+\frac{1}{4.6}-\frac{1}{6.8}+...+\frac{1}{16.18}-\frac{1}{18.20}\right)\)
\(4A=5.\left(\frac{1}{8}-\frac{1}{360}\right)\)
\(4A=5.\left(\frac{45}{360}-\frac{1}{360}\right)\)
\(4A=5.\frac{44}{360}\)
\(A=\frac{5.44}{360.4}\)
\(A=\frac{11}{72}\)
Tham khảo~
\(A=\frac{5}{2\cdot4\cdot6}+\frac{5}{4\cdot6\cdot8}+.....+\frac{5}{16\cdot18\cdot20}\)
\(\frac{4}{5}A=\frac{4}{2\cdot4\cdot6}+\frac{4}{4\cdot6\cdot8}+.........+\frac{4}{16\cdot18\cdot20}\)
\(\frac{4}{5}A=\frac{1}{2\cdot4}-\frac{1}{4\cdot6}+\frac{1}{4\cdot6}-\frac{1}{6\cdot8}+.........+\frac{1}{16\cdot18}-\frac{1}{18\cdot20}\)
\(\frac{4}{5}A=\frac{1}{2\cdot4}-\frac{1}{18\cdot20}\)
\(\frac{4}{5}A=\frac{1}{8}-\frac{1}{360}\)
\(\frac{4}{5}A=\frac{11}{90}\)
\(A=\frac{11}{90}:\frac{4}{5}=\frac{11}{72}\)
