\(\text{Ta có:}\) \(C=\frac{4}{2.4}+\frac{4}{4.6}+\frac{4}{6.8}+...+\frac{4}{2008.2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{2008.2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{2008}-\frac{1}{2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{1}{2}-\frac{1}{2010}\)
\(\Rightarrow\frac{1}{2}C=\frac{502}{1005}\)
\(\Rightarrow C=\frac{502}{1005}:\frac{1}{2}=\frac{1004}{1005}\)
Ta có: \(B=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}\)
\(\Rightarrow2B=\frac{2}{25.27}+\frac{2}{27.29}+...+\frac{2}{73.75}\)
\(\Rightarrow2B=\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+....+\frac{1}{73}-\frac{1}{75}\)
\(\Rightarrow B=\left(\frac{1}{25}-\frac{1}{75}\right):2\)
\(\Rightarrow B=\frac{1}{75}\)
Vậy \(B=\frac{1}{75}\)
\(C=\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{2008.2010}\)
\(\Rightarrow\frac{2}{4}C=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{2008}-\frac{1}{2010}\)
\(\Rightarrow\frac{2}{4}C=\frac{1}{2}-\frac{1}{2010}=\frac{502}{1005}\)
\(\Rightarrow C=\frac{502}{1005}:\frac{2}{4}=\frac{1004}{1005}\)
Vậy \(C=\frac{1004}{1005}\)
Ủng hộ tớ nha m.n ^_^
B = 1/25 - 1/27 + 1/27 - 1/29 + 1/29 - 1/31 +...+ 1/73 - 1/75
B = 1/25 - 1/75
B = 3/75 - 1/75 . B = 2/75
