\(\frac{1}{5×6}+\frac{1}{6×7}+\frac{1}{7×8}+...+\frac{1}{24×25}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{5}{25}-\frac{1}{25}\)

\(=\frac{4}{25}\)

\(\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+...+\frac{1}{24\times25}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)\(\left(=0,16\right)\)

\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+......+\frac{1}{24.25}\)

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+......+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}+\left(\frac{1}{6}-\frac{1}{6}+\frac{1}{7}-\frac{1}{7}+....+\frac{1}{25}-\frac{1}{25}\right)-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)

1/5×6 + 1/6×7 + 1/7×8 + ... + 1/24×25

= 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ... + 1/24 - 1/25

= 1/5 - 1/25

= 5/25 - 1/25

= 4/25

\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+....+\frac{1}{24}-\frac{1}{25}\)

\(=\frac{1}{5}-\frac{1}{25}\)

\(=\frac{4}{25}\)

                         \(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{24.25}\)

                      \(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

                     \(=\frac{1}{5}-\frac{1}{25}\) 

                   \(=\frac{5-1}{25}=\frac{4}{25}\)

                  Ủng hộ mk nha !!! ^_^

   \(\dfrac{1}{5\times6}+\dfrac{1}{6\times7}+\dfrac{1}{7\times8}+\dfrac{1}{8\times9}+\dfrac{1}{9\times10}\)

= \(\dfrac{1}{5}-\dfrac{1}{6}\times\dfrac{1}{6}-\dfrac{1}{7}\times\dfrac{1}{7}-\dfrac{1}{8}\times\dfrac{1}{8}-\dfrac{1}{9}\times\dfrac{1}{9}-\dfrac{1}{10}\)

= \(\dfrac{1}{5}-\dfrac{1}{10}\)  

= \(\dfrac{1}{10}\)

Bài tập cuối tuần 10

`1/[4xx5]+1/[5xx6]+1/[6xx7]+1/[7xx8]+1/[8xx9]+1/[9xx10]`

`=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10`

`=1/4-1/10`

`=10/40-4/40=6/40=3/20`

\(A=\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{7}-\dfrac{1}{8}=\dfrac{1}{2}-\dfrac{1}{8}=\dfrac{3}{8}\)

1/5-1/6+1/6-1/7+1/7-1/8+....+1/49-1/50

=1/5-1/50

=9/50

Đặt  \(A=\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}+\frac{1}{7x8}+\frac{1}{8x9}\)

\(A=\frac{3-2}{2x3}+\frac{4-3}{3x4}+\frac{5-4}{4x5}+\frac{6-5}{5x6}+\frac{7-6}{6x7}+\frac{8-7}{7x8}+\frac{9-8}{8x9}\)

\(A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

\(A=\frac{1}{2}-\frac{1}{9}=\frac{9}{18}-\frac{2}{18}=\frac{7}{18}\)

1/2x3 + 1/3x4 + 1/4x5 +1/5x6 +1/6x7+1/7x8 + 1/8x9 = 7/18

= 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12

= 1/3 - 1/12 = 1/4

Sai rồi bạn ạ

Phải là 1/3 nhân 4 chứ ko phải 1/3x4

Tra loi:

1/2x3+1/3x4+1/4x5+1/5x6+1/6x7+1/7x8+1/8x9

=1/2 - 1/3 + 1/3 - 1/4 +1/4 - 1/5 + 1/5 -1/6 +1/6 - 1/7 +1/7 -1/8+1/8 - 1/9

=1/2-(1/3-1/3)-(1/4-1/4)-(1/5-1/5)-(1/6-1/6)-(1/7-1/7)-(1/8-1/8)-1/9

=1/2-0-0-0-0-0-0-1/9

=1/2-1/9

=7/18

k cho minh nha!

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