Nhân cả tổng với 2/2.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

=\(\dfrac{6}{5}\)=\(1\dfrac{1}{5}\)

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

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

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

=\(\dfrac{5}{2}.\left(\dfrac{1}{2}-\dfrac{1}{48}\right)\)

=\(\dfrac{5}{2}.\dfrac{23}{48}\) = \(\dfrac{115}{96}\)

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

\(=5.\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{48.50}\right)\)

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

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

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

\(=\dfrac{5}{2}.\dfrac{24}{25}\)

\(=\dfrac{12}{5}\)

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

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

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

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

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

mình nghĩ nên nhân với 5/2

gọi tổng của 1+2+3+4+...+79 là M

                     2+3+4+...+80 là N

ta có A = M.N

từ 1 đến 79 hay từ 2 đến 80 có  (79-1) chia 1 + 1=79

M = (79+1).79 chia 2= 3160

N = (80+2).79chia 2= 3239

A = 3160 .3239 = 10235240

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

\(A=\frac{5}{2}\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{48.50}\right)\)

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

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

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

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

=\(\frac{1}{5}.\left(\frac{1}{2}.\frac{12}{25}\right)\)

=\(\frac{1}{5}.\frac{6}{25}=\frac{6}{125}\)

Vậy \(A=\frac{6}{125}\)

A = (5/2 - 5/4) + (5/4-5/6) +....+(5/48-5/50)

A = 5/2 + ( 5/4-5/4) +(5/6-5/6)+....+(5/48-5/48)+5/50

A = 5/2-5/50

A = 125/50-5/50

A = 120/50 = 12/5

\(\frac{5}{2.4}+\frac{5}{4.6}+...+\frac{5}{98.100}\)

= \(\frac{5}{2}-\frac{5}{4}+\frac{5}{4}-\frac{5}{6}+...+\frac{5}{98}-\frac{5}{100}\)

= \(\frac{5}{2}-\frac{5}{100}\)

= \(\frac{49}{50}\)

\(Q=\frac{5}{2.4}+\frac{5}{4.6}+...+\frac{5}{98.100}\)

    \(=5\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\right)\)

    \(=\frac{5}{2}.2.\left(\frac{1}{2.4}+\frac{1}{4.6}+...+\frac{1}{98.100}\right)\)

    \(=\frac{5}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+...+\frac{2}{98.100}\right)\)

    \(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+...+\frac{1}{98}-\frac{1}{100}\right)\)

    \(=\frac{5}{2}.\left(\frac{1}{2}-\frac{1}{100}\right)=\frac{5}{2}.\frac{49}{100}=\frac{49}{40}\)

\(\Rightarrow Q=\frac{49}{40}\)