\(\frac{1}{9.10}\)có x k bn?

k có x như trên đề thì hơi vl đấy.

phiền bn xem lại.

\(\frac{1}{1\cdot2}\times+\cdot\cdot\cdot+\frac{1}{9\cdot10}\times=\frac{18}{5}\)

\(\Rightarrow\left(\frac{1}{1\cdot2}+\cdot\cdot\cdot+\frac{1}{9\cdot10}\right)\times=\frac{18}{5}\)

\(\Rightarrow\left(1-\frac{1}{2}+\cdot\cdot\cdot+\frac{1}{9}-\frac{1}{10}\right)\times=\frac{18}{5}\)

\(\Rightarrow\left(1-\frac{1}{10}\right)\times=\frac{18}{5}\)

\(\Rightarrow\frac{9}{10}\times=\frac{18}{5}\)

\(\Rightarrow\times=\frac{18}{5}:\frac{9}{10}\)

\(\Rightarrow\times=4\)

\(\text{Đề }\Leftrightarrow\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right).\left(x-1\right)=x-\frac{1}{3}\)

=> \(\left(1-\frac{1}{10}\right).\left(x-1\right)=x-\frac{1}{3}\)

=> \(\frac{9}{10}.\left(x-1\right)=x-\frac{1}{3}\)

=> \(\frac{9x}{10}-\frac{9}{10}=\frac{3x-1}{3}\)

=> \(\frac{27x}{30}-\frac{27}{30}=\frac{10.\left(3x-1\right)}{30}\)

=> 27x - 27 = 30x - 10

=> 27x - 30x = -10 + 27

=> -3x = 17

=> x = -17/3.

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)
\(A=\left(1-\frac{1}{2}\right)+\left(\frac{1}{2}-\frac{1}{3}\right)+...+\left(\frac{1}{9}-\frac{1}{10}\right)\) 
\(A=1-\frac{1}{10}\)
\(A=\frac{9}{10}\)

dế mà em, giải thế này nè

A=1-1/2 +1/2-1/3 +1/3-1/4 +......+1/9-1/10

A=1-1/10+9/10

\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10}\right)\cdot100-\left[\frac{5}{2}:\left(X+\frac{206}{100}\right)\right]:\frac{1}{2}=89\\ \left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\cdot100-\left[\frac{5}{2}:\left(X+\frac{206}{100}\right)\right]:\frac{1}{2}=89\\ \left(1-\frac{1}{10}\right)\cdot100-\left[\frac{5}{2}:\left(X+\frac{206}{100}\right)\right]:\frac{1}{2}=89\\ \frac{9}{10}\cdot100-\left[\frac{5}{2}:\left(X+\frac{206}{100}\right)\right]:\frac{1}{2}=89\\ 90-\left[\frac{5}{2}:\left(X+\frac{206}{100}\right)\right]:\frac{1}{2}=89\\ \left[\frac{5}{2}:\left(X+\frac{206}{100}\right)\right]:\frac{1}{2}=1\\ \frac{5}{2}:\left(X+\frac{206}{100}\right)=\frac{1}{2}\\ X+\frac{206}{100}=5\\ X=\frac{500}{100}-\frac{206}{100}\\ X=\frac{294}{100}=\frac{147}{50}\)

Vậy \(X=\frac{147}{50}\)

( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ......+ 1/9 - 1/10) . 100 - [ 5/2 : ( x + 103/50 ) ] = 89 . 1/2

( 1 - 1/10) . 100 - [ 5/2 : ( x + 103/50 ) ] = 89/2

90 - 5/2 : ( x + 103/50 ) = 89/2

5/2 : ( x + 103/50 ) = 90 - 89/2

5/2 : ( x + 103/50 ) = 91/2

x + 103/50 = 5/2 : 91/2

x + 103/50 = 5/91

x = 5/91 - 103/50

x = -9,123/4550

\(=\frac{1}{1.2}-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{10}\)

\(=\frac{1}{10}\)

(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-......+1/9-1/10)

1-1/10=9/10

nhớ cho mk

Bài 1

a) \(P=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)

\(=1-\frac{1}{10}\)

\(=\frac{10}{10}-\frac{1}{10}=\frac{9}{10}\)

b) \(S=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\)

\(=\frac{1}{3}-\frac{1}{99}\)

\(=\frac{33}{99}-\frac{1}{99}\)

\(=\frac{32}{99}\)

c)\(Q=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{10}{20}-\frac{1}{20}\)

\(=\frac{9}{20}\)

Tk mình nha!!

Câu 2:

\(P=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...\left(1+\frac{1}{99}\right)\)

\(=\left(\frac{2}{2}+\frac{1}{2}\right).\left(\frac{3}{3}+\frac{1}{3}\right).\left(\frac{4}{4}+\frac{1}{4}\right)...\left(\frac{99}{99}+\frac{1}{99}\right)\)

\(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{100}{99}\)

\(=\frac{3\cdot4\cdot5...100}{2.3.4...99}\)

\(=\frac{3\cdot100}{2}\)

\(=\frac{300}{2}=150\)

\(\frac{1}{1.2}-\frac{1}{2.3}-\frac{1}{3.4}-......-\frac{1}{9.10}\)

\(=\frac{1}{2}-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+.....+\frac{1}{9}-\frac{1}{10}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{10}\right)\)

\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{10}=\frac{1}{10}\)

Kết quả là \(\frac{9}{10}\)

Đúng 100% k mình nha

giúp mk mk tích cho

A=10(1/1.2+5/2.3+...+89/9.10)

A=10(1/2+5/6+...+89/90)

A=10[(1-1/2)+(1-1/6)+.....+(1-1/90)

A=10(1-1/2+1-1/6+...+1-1/90)

A=10[(1+1+...+1)-(1/2+1/6+...+1/90)

           9 chữ số 1

A=10[9-(1/1.2+1/2.3+...+1/9.10)]

A=10[9-(1-1/2+1/2-1/3+...+1/9-1/10)]

A=10[9-(1-1/10)]

A=10(9-9/10)

A=90-9=81