\(\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...........+\frac{1}{98.100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}=\frac{49}{100}\)

cho mình nha!

Nhân cả tổng với 2/2.

\(\frac{5}{2.4}+\frac{5}{4.6}+\frac{5}{6.8}+....+\frac{5}{48.50}\)

\(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{48}-\frac{1}{50}\right)\)

\(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{50}\right)\)

\(=\frac{5}{2}.\frac{12}{25}=\frac{6}{5}\)

\(\frac{5}{2.4}+\frac{5}{4.6}+\frac{5}{6.8}+...+\frac{5}{48.50}\)

\(=\frac{2}{5}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{48.50}\right)\)

\(=\frac{2}{5}.\left(\frac{4-2}{2.4}+\frac{6-4}{4.6}+\frac{8-6}{6.8}+...+\frac{50-48}{48.50}\right)\)

\(=\frac{2}{5}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{48}-\frac{1}{50}\right)\)

\(=\frac{2}{5}.\left(\frac{1}{2}-\frac{1}{50}\right)\)

\(=\frac{2}{5}.\frac{12}{25}\)

\(=\frac{24}{125}\)

\(B=\frac{3}{2.4}-\frac{5}{4.6}+\frac{7}{6.8}-\frac{9}{8.10}+...+\frac{2019}{2018.2020}\)

\(B=\frac{3}{2.1.2.2}-\frac{5}{2.2.2.3}+\frac{7}{2.3.2.4}-\frac{9}{2.4.2.5}+...+\frac{2019}{2.1009.2.1010}\)

\(B=\frac{1}{4.}.\left(\frac{3}{1.2}-\frac{5}{2.3}+\frac{7}{3.4}-\frac{9}{4.5}+...+\frac{2019}{1009.1010}\right)\)

\(B=\frac{1}{4.}.\left(\frac{3}{1}-\frac{3}{2}-\frac{5}{2}+\frac{5}{3}+\frac{7}{3}-\frac{7}{4}-\frac{9}{4}+\frac{9}{5}+...+\frac{2019}{1009}-\frac{2019}{1010}\right)\)

\(B=\frac{1}{4.}.\left(\frac{3}{1}-4+4-4+4-...+4-\frac{2019}{1010}\right)\)

\(B=\frac{1}{4.}.\left(\frac{3}{1}-\frac{2019}{1010}\right)=\frac{1011}{4040}\)

\(\frac{5}{2.4}+\frac{5}{4.6}+\frac{5}{6.8}+...+\frac{5}{48.50}\)

\(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{48}-\frac{1}{50}\right)\)

\(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{50}\right)\)

\(=\frac{5}{2}.\frac{12}{25}\)

\(=\frac{6}{5}\)

mình nghĩ nên nhân với 5/2

=1/2-1/4+1/4-1/6+....+1/98-1/100

=1/2-1/100

=49/100

=1/2-1/4+1/4-1/6+ ... +1/98-1/100

=1/2-1/100

=49/100

C= \(\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+....+\frac{2}{98.100}\right)\)

  = \(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+....+\frac{1}{98}-\frac{1}{100}\right)\)

  = \(\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)

  = \(\frac{1}{2}.\left(\frac{50}{100}-\frac{1}{100}\right)\)

  = \(\frac{1}{2}.\frac{49}{100}\)

  = \(\frac{49}{200}\)

 \(A=\frac{-1}{2.4}+\frac{-1}{4.6}+\frac{-1}{6.8}+...+\frac{-1}{98.100}\Leftrightarrow.\)\(-2A=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\Leftrightarrow.\)

\(-2A=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{97}-\frac{1}{98}+\frac{1}{98}-\frac{1}{100}\Leftrightarrow.\)

\(-2A=\frac{1}{2}-\frac{1}{100}\Leftrightarrow-2A=\frac{49}{100}\Leftrightarrow A=\frac{-49}{200}.\)

ĐÁP SỐ :   \(A=\frac{-49}{200}.\)

\(\frac{-49}{200}\)

\(A=\frac{-1}{2.4}+\frac{-1}{4.6}+\frac{-1}{6.8}+...+\frac{-1}{98.100}\)

\(\Leftrightarrow A=\frac{-1}{4}\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{98.100}\right)\)

\(\Leftrightarrow A=\frac{-1}{4}\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(\Leftrightarrow A=\frac{-1}{4}\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(\Leftrightarrow A=\frac{-1}{4}.\frac{49}{50}\)

\(\Leftrightarrow A=\frac{-49}{200}\)

\(\frac{4}{2.4}+\frac{4}{4.6}+...+\frac{4}{98.100}\)

\(=2.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=2.\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=2.\frac{49}{100}\)

\(=\frac{49}{50}\)

\(=2\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\right)\)

\(=2\cdot\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=2\cdot\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=2\cdot\frac{49}{100}\)

\(=\frac{49}{50}\)

\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(=\frac{1}{2}.\frac{49}{100}\)

\(=\frac{49}{200}\)

Giúp mk mấy bài nhaEdowa Conan

\(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\)

\(=\frac{1}{2}-\frac{1}{100}\)

\(=\frac{49}{100}\)