`A=1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+1/(6xx7)+1/(7xx8)`

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

`=1/2-1/8`

`=4/8-1/8`

`=3/8`

Vậy `A=3/8`

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

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

= \(\dfrac{1}{5}-\dfrac{1}{10}\)  

= \(\dfrac{1}{10}\)

Bài tập cuối tuần 10

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

= 1/3 - 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1/5x6+1/6x7+1/7x8+...+1/2019x2020

= 6/5+7/6+8/7+...+2020/2019

Rút gọn cho nhau ta còn 2020/5=404

1/5 x 6 + 1/6 x7 + 1/7 x8 + ... + 1/2019 - 1/ 2020

=1/5 -1/6 +1/6 -1/7 + 1/7 - 1/8 + ... + 1/2019 - 1/2020

Sau khi giản ước, ta còn:

1/5 - 1/2020 = 403/2020.

                     Đáp số: 403/2020

Mình xin lôĩ, mình nhìn nhầm đề mong bạn thông cảm.

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 !!! ^_^

`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`

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