Đặt \(A=\frac{2}{10\cdot12}+\frac{2}{12\cdot14}+\frac{2}{14\cdot16}+...+\frac{2}{48\cdot50}\)
\(A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{48}-\frac{1}{50}\)
\(A=\frac{1}{10}-\frac{1}{50}=\frac{5}{50}-\frac{1}{50}=\frac{4}{50}=\frac{2}{25}\)
Vậy \(A=\frac{2}{25}\)
= \(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{48}-\frac{1}{50}\)
= \(\frac{1}{10}-\frac{1}{50}\)= \(\frac{2}{25}\)
2/10.12+2/12.14+2/14.16+...+2/48.50
=1/10-1/12+1/12-1/14+1/14-1/16+...+1/48-1/50
=( 1/10-1/50 )+( 1/12-1/12 )+( 1/14-1/14 )+...+( 1/48-1/48 )
=( 5/50-1/50 )+0+0+...+0
=4/50
=2/25
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