\(D=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+\frac{1}{80}+........+\frac{1}{1520}\)
\(D=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+........+\frac{1}{38.40}\)
\(2D=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+......+\frac{2}{38.40}\)
\(2D=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-.......-\frac{1}{40}\)
\(2D=1-\frac{1}{40}\)
\(2D=\frac{40}{40}-\frac{1}{40}\)
\(2D=\frac{39}{40}\)
\(D=\frac{39}{40}:2=\frac{39}{40}.\frac{1}{2}=\frac{39}{80}\)
Vậy ....
\(D=\frac{1}{8}+\frac{1}{24}+\frac{1}{48}+...+\frac{1}{1520}\)
\(D=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{38.40}\)
\(D=\frac{1}{2}\times\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{38.40}\right)\)
\(D=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{38}-\frac{1}{40}\right)\)
\(D=\frac{1}{2}\times\left(\frac{1}{2}-\frac{1}{40}\right)\)
\(D=\frac{1}{2}\times\frac{19}{40}\)
\(D=\frac{19}{80}\)
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