Question

1. Tính:

a.\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\)

b.\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\)

2. Tìm x , biết:

a. \(\dfrac{2}{5}+\dfrac{4}{5}x-\dfrac{7}{5}=\dfrac{9}{5}\)

b. \(\dfrac{2}{5}x-\dfrac{6}{4}=\dfrac{8}{5}\)

bài này ko được coppy trên mạng

Answer 1

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)\(\dfrac{2}{5}x-\dfrac{6}{4}=\dfrac{8}{5}\)

\(\dfrac{2}{5}x=\dfrac{8}{5}+\dfrac{6}{4}\)

\(\dfrac{2}{5}x=\dfrac{31}{10}\)

\(x=\dfrac{31}{10}:\dfrac{2}{5}\)

\(x=\dfrac{31}{4}\)

Answer 2

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

Answer 3

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 = \(\dfrac{31}{4}\)

Answer 4

trên mạng có tìm được đâu mà coppy.

Answer 5

Câu 1 mình cho bn công thức, bn tự làm nhé!

\(\dfrac{a}{n+\left(n+a\right)}=\dfrac{1}{n}-\dfrac{1}{n+a}\)

Answer 6

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}=1-\dfrac{1}{10}=\dfrac{9}{10}\)

Answer 7

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 \(x=\dfrac{31}{4}\).

Answer 8

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

Answer 9

bài này dễ mà bạn