1)Tính
a)\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+..........+\dfrac{1}{9.10}\)
=\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.....+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=1-\dfrac{1}{10}\)
\(=\dfrac{9}{10}\)
b)\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+.........+\dfrac{1}{99.100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+..............+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)
2) tìm x
\(a\)) \(\dfrac{2}{5}+\dfrac{4}{5}x-\dfrac{7}{5}\)\(=\dfrac{9}{5}\)
\(\dfrac{4}{5}x+\dfrac{7}{5}=\dfrac{9}{5}-\dfrac{2}{5}\)
\(\dfrac{4}{5}x+\dfrac{7}{5}=\dfrac{7}{5}\)
\(\dfrac{4}{5}x=\dfrac{7}{5}-\dfrac{7}{5}\)
\(\dfrac{4}{5}x=0\)
\(x=0:\dfrac{4}{5}\)
\(x=0\)
b)\(\dfrac{2}{5}x-\dfrac{6}{4}=\dfrac{8}{5}\)
\(\dfrac{2}{5}x=\dfrac{8}{5}+\dfrac{6}{4}\)
\(\dfrac{2}{5}x=\dfrac{31}{10}\)
\(x=\dfrac{31}{10}:\dfrac{2}{5}\)
\(x=\dfrac{31}{4}\)
1. Tính:
a. \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\)
= \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
= \(\dfrac{1}{1}-\dfrac{1}{10}\)
= \(\dfrac{10}{10}-\dfrac{1}{10}\)
= \(\dfrac{9}{10}\)
b. \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)
= \(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
= \(\dfrac{1}{1}-\dfrac{1}{100}\)
= \(\dfrac{100}{100}-\dfrac{1}{100}\)
= \(\dfrac{99}{100}\)
2. Tìm x, biết:
a. \(\dfrac{2}{5}+\dfrac{4}{5}x-\dfrac{7}{5}=\dfrac{9}{5}\)
\(\dfrac{4}{5}x-\dfrac{7}{5}=\dfrac{9}{5}-\dfrac{2}{5}\)
\(\dfrac{4}{5}x-\dfrac{7}{5}=\dfrac{7}{5}\)
\(\dfrac{4}{5}x=\dfrac{7}{5}+\dfrac{7}{5}\)
\(\dfrac{4}{5}x=\dfrac{14}{5}\)
\(x=\dfrac{14}{5}:\dfrac{4}{5}\)
\(x=\dfrac{14}{5}.\dfrac{5}{4}\)
\(x=14.\dfrac{1}{4}\)
\(x=\dfrac{14}{4}\)
Vậy \(x=\dfrac{14}{4}\)
b. \(\dfrac{2}{5}x-\dfrac{6}{4}=\dfrac{8}{5}\)
\(\dfrac{2}{5}x=\dfrac{8}{5}+\dfrac{6}{4}\)
\(\dfrac{2}{5}x=\dfrac{32}{20}+\dfrac{30}{20}\)
\(\dfrac{2}{5}x=\dfrac{62}{20}\)
\(\dfrac{2}{5}x=\dfrac{31}{10}\)
\(x=\dfrac{31}{10}:\dfrac{2}{5}\)
\(x=\dfrac{31}{10}.\dfrac{5}{2}\)
\(x=\dfrac{31}{2}.\dfrac{2}{2}\)
\(x=\dfrac{31}{2}.1\)
\(x=\dfrac{31}{2}\)
Vậy \(x=\dfrac{31}{2}\)
bài này mk tự làm ko sao chép trên mạng
nếu thấy đúng thì tick đúng cho mk nha
1 . Tính
a . \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + ... + \(\dfrac{1}{9.10}\)
= 1 - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + ... + \(\dfrac{1}{9}\) - \(\dfrac{1}{10}\)
= 1 - \(\dfrac{1}{10}\)
= \(\dfrac{9}{10}\)
b . \(\dfrac{1}{1.2}\) + \(\dfrac{1}{2.3}\) + \(\dfrac{1}{3.4}\) + ... + \(\dfrac{1}{99.100}\)
= 1 - \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{4}\) + ... + \(\dfrac{1}{99}\) - \(\dfrac{1}{100}\)
= 1 - \(\dfrac{1}{100}\)
=\(\dfrac{99}{100}\)
2 . Tìm x , biết :
a . \(\dfrac{2}{5}\) + \(\dfrac{4}{5}\)x - \(\dfrac{7}{5}\) = \(\dfrac{9}{5}\)
\(\dfrac{2}{5}\) - \(\dfrac{7}{5}\) + \(\dfrac{4}{5}\)x = \(\dfrac{9}{5}\)
-1 + \(\dfrac{4}{5}\)x = \(\dfrac{9}{5}\)
\(\dfrac{4}{5}\)x = \(\dfrac{9}{5}\) + 1 ( Quy tắc chuyển vế )
\(\dfrac{4}{5}\)x = \(\dfrac{14}{5}\)
=> 4.x = 14
=> x = 14 : 4
=> x = 3,5
b . \(\dfrac{2}{5}\)x - \(\dfrac{6}{4}\) = \(\dfrac{8}{5}\)
\(\dfrac{2}{5}\)x = \(\dfrac{8}{5}\) + \(\dfrac{6}{4}\)
\(\dfrac{2}{5}\)x = \(\dfrac{31}{10}\)
x = \(\dfrac{31}{10}\) : \(\dfrac{2}{5}\)
x = \(\dfrac{31.5}{10.2}\)
x = \(\dfrac{31.1}{2.2}\)
x = \(\dfrac{31}{4}\)
Câu 1 mình cho bn công thức, bn tự làm nhé!
\(\dfrac{a}{n+\left(n+a\right)}=\dfrac{1}{n}-\dfrac{1}{n+a}\)
\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}=1-\dfrac{1}{10}=\dfrac{9}{10}\)
Bài 1:
a) \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=1-\dfrac{1}{10}\)
\(=\dfrac{10}{10}-\dfrac{1}{10}\)
\(=\dfrac{9}{10}\)
b) \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{99\cdot100}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{99}-\dfrac{1}{100}\)
\(=1-\dfrac{1}{100}\)
\(=\dfrac{100}{100}-\dfrac{1}{100}\)
\(=\dfrac{99}{100}\)
Bài 2:
a) \(\dfrac{2}{5}+\dfrac{4}{5}x-\dfrac{7}{5}=\dfrac{9}{5}\)
\(\Rightarrow-1+\dfrac{4}{5}x=\dfrac{9}{5}\)
\(\Rightarrow\dfrac{4}{5}x=\dfrac{9}{5}+1\)
\(\Rightarrow\dfrac{4}{5}x=\dfrac{14}{5}\)
\(\Rightarrow x=\dfrac{14}{5}:\dfrac{4}{5}\)
\(\Rightarrow x=\dfrac{7}{2}\)
Vậy \(x=\dfrac{7}{2}\).
b) \(\dfrac{2}{5}x-\dfrac{6}{4}=\dfrac{8}{5}\)
\(\Rightarrow\dfrac{2}{5}x=\dfrac{8}{5}+\dfrac{6}{4}\)
\(\Rightarrow\dfrac{2}{5}x=\dfrac{31}{10}\)
\(\Rightarrow x=\dfrac{31}{10}:\dfrac{2}{5}\)
\(\Rightarrow x=\dfrac{31}{4}\)
Vậy \(x=\dfrac{31}{4}\).
1a\((\dfrac{1}{1}-\dfrac{1}{10})\div1(khoảngcách)\)
1b\((\dfrac{1}{1}-\dfrac{1}{100})\div1(1=2-1ởmẫu)\)
2a. \(\dfrac{2}{5}+\dfrac{4}{5}x-\dfrac{7}{5}=\dfrac{9}{5}\)
\(\Leftrightarrow\dfrac{2}{5}+\dfrac{4}{5}x=\dfrac{9}{5}+\dfrac{7}{5}=\dfrac{16}{5}\)
\(\Leftrightarrow\dfrac{4}{5}x=\dfrac{16}{5}-\dfrac{2}{5}=\dfrac{14}{5}\)
\(\Rightarrow x=\dfrac{14}{5}\div\dfrac{4}{5}=\dfrac{7}{2}\)
2b.\(\dfrac{2}{5}x-\dfrac{6}{4}=\dfrac{8}{5}\)
\(\Leftrightarrow\dfrac{2}{5}x=\dfrac{8}{5}+\dfrac{6}{4}=\dfrac{31}{10}\)
\(\Rightarrow x=\dfrac{31}{10}\div\dfrac{2}{5}=\dfrac{31}{4}\)
mk làm như vậy nếu thấy đúng thì tick cho mk nhé!!chúc bạn học giỏi