Giúp mik

1-1/10=9/10

B = \(\dfrac{1}{1}.2+\dfrac{1}{2}.3+..........+\dfrac{1}{9}.10\) Lên lớp 6 dấu chấm là dấu nhân

B = \(\dfrac{2}{1}+\dfrac{3}{2}+\dfrac{4}{3}+\dfrac{5}{4}+\dfrac{6}{5}+\dfrac{7}{6}+\dfrac{8}{7}+\dfrac{9}{8}+\dfrac{10}{9}\)

B = \(\dfrac{1+1}{1}\)  + \(\dfrac{2+1}{2}+\dfrac{4+1}{4}+\dfrac{5+1}{5}+\dfrac{6+1}{6}+\dfrac{7+1}{7}+\dfrac{8+1}{8}+\dfrac{9+1}{9}\) 

B =  \(\dfrac{1}{1}+\dfrac{1}{1}-\dfrac{2}{2}+\dfrac{1}{2}-\dfrac{3}{3}+\dfrac{1}{3}-\dfrac{4}{4}+\dfrac{1}{4}-\dfrac{5}{5}+\dfrac{1}{5}-\dfrac{6}{6}+\dfrac{1}{6}-\dfrac{7}{7}+\dfrac{1}{7}-\dfrac{8}{8}+\dfrac{1}{8}+\dfrac{9}{9}+\dfrac{1}{9}\)

B = 10 + ( \(\dfrac{1}{1.2}+\dfrac{1}{1.3}+\dfrac{1}{2.4}+\dfrac{1}{1.5}+\dfrac{1}{2.3}+\dfrac{1}{1.7}+\dfrac{1}{2.4}+\dfrac{1}{1.9}\) )

B = 10 + ( \(\dfrac{1}{1}.\dfrac{1}{2}+\dfrac{1}{1}.\dfrac{1}{3}+\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{1}.\dfrac{1}{5}+\dfrac{1}{2}.\dfrac{1}{3}+\dfrac{1}{1}.\dfrac{1}{7}+\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{1}.\dfrac{1}{9}\) )

B = 10 + ( \(\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{9}\) ) 

B = 10 + 143/315 

B = \(\dfrac{3613}{3150}\)

mik nghĩ là mình sai bạn à

1/1 x 2 + 1/2 x 3 + 1/3 x 4 + .... + 1/9 x 10

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

= 1 - 1/10

= 9/10

\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{9\times10}\\ =1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\\ =1-\dfrac{1}{10}\\ =\dfrac{9}{10}\)

9/10 nha

Ta đặt biểu thức là:

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

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

A = 1 - 1/10

A = 9/10

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

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

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

 = 1/1 x 2 + 1/2 x 3 + 1/3 x 4 + .... + 1/9 x 10

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

 = 1 - 1/10

 = 9/10

\(A=\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}....\frac{1}{9x10}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}...+\frac{1}{9}-\frac{1}{10}=\frac{9}{10}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}=\frac{1}{1}-\frac{1}{10}=\frac{9}{10}\)

\(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}=1-\dfrac{1}{10}=\dfrac{9}{10}\)

\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{9\times10}\)
\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\)
\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)
#kễnh

=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+............+1/9+1/10

=1-1/10

=10/10-1/10

=9/10

Bài làm:

  \(\frac{1}{1\times2}+\frac{1}{2\times3}\)\(+\frac{1}{3\times4}+\frac{1}{4\times5}\)\(+...\frac{1}{9\times10}\)

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

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

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

\(\left(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+...+\dfrac{1}{9\times10}\right)\times x=\dfrac{3}{4}\)

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

                                     \(\left(1-\dfrac{1}{10}\right)\times x=\dfrac{3}{4}\) 

                                                 \(\dfrac{9}{10}\times x=\dfrac{3}{4}\) 

                                                             \(x=\dfrac{3}{4}\times\dfrac{10}{9}\) 

                                                             \(x=\dfrac{5}{6}\)

1/1*2+1/2*3+1/3*4+...+1/9*10

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

=1-1/10

=9/10

nho k cho minh voi nhe

\(\frac{1}{1.2}\)+ \(\frac{1}{2.3}\)+ \(\frac{1}{3.4}\)+ ......... + \(\frac{1}{7.8}\)+ \(\frac{1}{8.9}\)+ \(\frac{1}{9.10}\)

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

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

9/10 nha