\(C=\frac{5}{1.3}+\frac{5}{3.5}+\frac{5}{5.7}+...+\frac{5}{45.47}\)
\(C=\frac{5}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{45}-\frac{1}{47}\right)\)
\(C=\frac{5}{2}.\left(1-\frac{1}{47}\right)\)
\(C=\frac{5}{2}.\frac{46}{47}\)
\(C=\frac{115}{47}\)
\(C=\frac{5}{1\cdot3}+\frac{5}{3\cdot5}+\frac{5}{5\cdot7}+...+\frac{5}{45\cdot47}\)
\(C=\frac{5}{2}\cdot\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{45\cdot47}\right)\)
\(C=\frac{5}{2}\cdot\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{45}-\frac{1}{47}\right)\)
\(C=\frac{5}{2}\cdot\left(1-\frac{1}{47}\right)\)
\(C=\frac{5}{2}\cdot\frac{46}{47}\)
\(C=\frac{115}{47}\)
Ta có :
\(C=\frac{5}{1.3}+\frac{5}{3.5}+...+\frac{5}{45.47}\)
\(\Rightarrow C=\frac{5}{2}.\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{45.47}\right)\)
\(\Rightarrow C=\frac{5}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{45}-\frac{1}{47}\right)\)
\(\Rightarrow C=\frac{5}{2}.\left(1-\frac{1}{47}\right)\)
\(\Rightarrow C=\frac{5}{2}.\frac{46}{47}\)
\(\Rightarrow C=\frac{115}{47}\)
Vậy \(C=\frac{115}{47}\)
~ Ủng hộ nhé
