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\(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+\frac{1}{13.14}+........+\frac{1}{78.79}\)

\(=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+............+\frac{1}{78}-\frac{1}{79}\)

\(=\frac{1}{10}-\frac{1}{79}=\frac{69}{790}\)

Dấu này * là dấu nhân

Một năm rồi không có ai trả lời à 

THấy cx thương nhưng mk nhìn cái đề thì dài thật cx khó có ai có thời gian mà giải

a) = 1/10 - 1/11 + 1/11 -1/12 + 1/12 - 1/13 +1/13 1/14 +...+ 1/78 - 1/79

= 1/10 - 1/79

= máy tính ok

mấy câu khác bn làm tương tự là đc nhưng nhớ nhanh thêm khoảng cách giữa các mẫu nha

a)\(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{78.79}=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{78}-\frac{1}{79}=\frac{1}{10}-\frac{1}{79}=\frac{69}{790}\)

b) \(\frac{8}{7.9}+\frac{8}{9.11}+...+\frac{8}{133.135}=4\left(\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{133.135}\right)\)

\(=4\left(\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{133}-\frac{1}{135}\right)=4\left(\frac{1}{7}-\frac{1}{135}\right)=4.\frac{128}{945}=\frac{456}{945}\)

c) \(\frac{12}{8.11}+\frac{12}{11.14}+...+\frac{12}{503.506}=4\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{503.506}\right)\)

\(=4\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{503}-\frac{1}{506}\right)=4\left(\frac{1}{8}-\frac{1}{506}\right)=\frac{249}{506}\)

d) \(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{391.394}=\frac{1}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{391.394}\right)\)

\(=\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{391}-\frac{1}{394}\right)=\frac{1}{3}.\left(\frac{1}{4}-\frac{1}{394}\right)=\frac{1}{3}.\frac{195}{788}=\frac{65}{788}\)

e) \(\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{602.605}=\frac{4}{3}.\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\right)\)

\(=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\right)=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{605}\right)=\frac{4}{3}.\frac{24}{121}=\frac{32}{121}\)

g) Sửa đề\(1+\frac{1}{3}+\frac{1}{6}+...+\frac{1}{820}=2\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{1640}\right)=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{40.41}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{40}-\frac{1}{41}\right)=2\left(1-\frac{1}{41}\right)=2.\frac{40}{41}=\frac{80}{41}\)

Bài làm:

a) \(\frac{1}{10.11}+\frac{1}{11.12}+...+\frac{1}{78.79}\)

\(=\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+...+\frac{1}{78}-\frac{1}{79}\)

\(=\frac{1}{10}-\frac{1}{79}=\frac{69}{790}\)

b) \(\frac{8}{7.9}+\frac{8}{9.11}+...+\frac{8}{133.135}\)

\(=4\left(\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{133.135}\right)\)

\(=4\left(\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{133}-\frac{1}{135}\right)\)

\(=4\left(\frac{1}{7}-\frac{1}{135}\right)\)

\(=4.\frac{128}{945}=\frac{512}{945}\)

c) \(\frac{12}{8.11}+\frac{12}{11.14}+...+\frac{12}{503.506}\)

\(=4\left(\frac{3}{8.11}+\frac{3}{11.14}+...+\frac{3}{503.506}\right)\)

\(=4\left(\frac{1}{8}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+...+\frac{1}{503}-\frac{1}{506}\right)\)

\(=4\left(\frac{1}{8}-\frac{1}{506}\right)\)

\(=4.\frac{249}{2024}=\frac{249}{506}\)

d) \(\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{391.394}\)

\(=\frac{1}{3}\left(\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{391.394}\right)\)

\(=\frac{1}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{391}-\frac{1}{394}\right)\)

\(=\frac{1}{3}\left(\frac{1}{4}-\frac{1}{394}\right)\)

\(=\frac{1}{3}.\frac{195}{788}=\frac{65}{788}\)

e) \(\frac{4}{5.8}+\frac{4}{8.11}+...+\frac{4}{602.605}\)

\(=\frac{4}{3}\left(\frac{3}{5.8}+\frac{3}{8.11}+...+\frac{3}{602.605}\right)\)

\(=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{11}+...+\frac{1}{602}-\frac{1}{605}\right)\)

\(=\frac{4}{3}\left(\frac{1}{5}-\frac{1}{605}\right)\)

\(=\frac{4}{3}.\frac{24}{121}=\frac{32}{121}\)

g) Phải sửa \(\frac{1}{802}\)  thành \(\frac{1}{820}\) nhé

\(1+\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{820}\)

\(=1+\frac{1}{1.3}+\frac{1}{2.3}+\frac{1}{2.5}+...+\frac{1}{41.20}\)

\(=2\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{40.41}\right)\)

\(=2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{40}-\frac{1}{41}\right)\)

\(=2\left(1-\frac{1}{41}\right)\)

\(=2.\frac{40}{41}=\frac{80}{41}\)

a) Dấu hiệu là điểm bài thi học kì của 100 học sinh lớp 7 của một trường Trung học Cơ Sở Hòa Bình. Số các dấu hiệu là 100
b) Bảng tần số
 

Nhận xét: Giá trị lớn nhất là 19, giá trị nhỏ nhất là 1; tần số lớn nhất là 13, tần số nhỏ nhất là 1.

a: =-5-7-8-3=-26

b: =-4-2-5-6=-17

c: =-8-11-4-2=-25

d: -9-15-6-3=-30

e: =-12-9-3-8=-32

`4/7+4`

`=4/7+4/1`

`=4/7+28/7`

`=32/7`

__

`3+6/11`

`=33/11+6/11`

`=39/11`

__

`3-5/7`

`=3/1-5/7`

`=21/7-5/7`

`=16/7`

__

`21/9-2`

`=21/9-18/9`

`=3/9`

`=1/3`

__

`15/24+2`

`=15/24+48/24`

`=63/24`

`=21/16`

__

`63/45-20/25`

`=63/45-4/5`

`=63/45-36/45`

`=27/45`

`=9/15`

__

`3/4-2/8`

`=3/4-1/4`

`=2/4`

__

`6/7-5/8`

`=48/56-35/56`

`=13/56`

__

`37/45-5/9`

`=37/45-25/45`

`=12/45`

`=4/15`

__

`46/39-11/13`

`=46/39-33/39`

`=13/39`

`=1/2`

__

`5/12+3/4+1/3`

`=5/12+9/12+4/12`

`=14/12+4/12`

`=18/12`

`=3/2`

__

`1/2+3/7+11/14`

`=7/14+6/14+11/14`

`=13/14+11/14`

`=24/14`

`=12/7`

__

`7/10-(1/5+1/4)`

`=7/10-(4/20+5/20)`

`=7/10-9/20`

`=14/20-9/20`

`=5/20`

`=1/4`

__

`15/4-2/3-3/4`

`=(15/4-3/4)-2/3`

`=12/4-2/3`

`=3-2/3`

`=9/3-2/3`

`=7/3`

lấy máy tính ra mà tính

đc thì đã tốt