\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+....+\frac{2}{575}+\frac{2}{675}\)
\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{23\times25}+\frac{2}{25\times27}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)
Vậy ....
\(\frac{2}{15}+\frac{2}{35}+\frac{2}{69}+........+\frac{2}{575}+\frac{2}{675}\)
\(=\frac{2}{3\times5}+\frac{2}{5\times7}+........+\frac{2}{23\times25}+\frac{2}{25\times27}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.......+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}\)
\(=\frac{8}{27}\)
\(\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+\frac{2}{99}+...+\frac{2}{575}+\frac{2}{675}\)
\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+\frac{2}{9\times11}+...+\frac{2}{23\times25}+\frac{2}{25\times27}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{25}+\frac{1}{25}-\frac{1}{27}\)
\(=\frac{1}{3}-\frac{1}{27}\)
\(=\frac{8}{27}\)
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