Ta có: \(A=-\frac{4}{20}-\frac{4}{30}-\frac{4}{42}-\frac{4}{56}-\frac{4}{72}-\frac{4}{90}\)

   \(\Leftrightarrow A=-4.\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

   \(\Leftrightarrow A=-4.\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

   \(\Leftrightarrow A=-4.\left(\frac{1}{4}-\frac{1}{10}\right)\)

   \(\Leftrightarrow A=-4.\left(\frac{5-2}{20}\right)\)

   \(\Leftrightarrow A=-4.\frac{3}{20}=-\frac{3}{5}\)

Vậy \(\Leftrightarrow A=-\frac{3}{5}\)

thanks

A=-4/4.5+-4/5.6+-4/6.7+-4/7.8+-4/8.9+-4/9.10

-1/4A=1/4.5+1/5.6+1/6.7+1/7.8+1/8.9+1/9.10

-1/4A=1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10

-1/4A=1/4-1/10

-1/4A=3/20

A=-3/5

thanks

Ta có : A = -4/20+-4/30+-4/42+-4/56+-4/72+-4/90

                = -4/4.5+-4/5.6+-4/6.7 +-4/7.8+-4/8.9+-4/9.10

                 =-4/4-(-4/5)+(-4/5)-(-4/6)+......+(-4/9)-(-4/10)

                  =-4/4-(-4/10)

                 =-3/5

# chúc bạn học tốt #

\(A=\frac{-4}{20}+\frac{-4}{30}+\frac{-4}{42}+...+\frac{-4}{90}\)

     =\(-4\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}\right)\)

    =-4\(\left(\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{9.10}\right)\)

  =-4\(\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{9}-\frac{1}{10}\right)\)

=-4\(\left(\frac{1}{4}-\frac{1}{10}\right)\)

=-4.\(\frac{3}{20}\)=\(\frac{-3}{5}\)

a)1/2 + 5/6 + 11/12 + 19/20 + 29/30 + 41/42 + 55/56 + 71/72+89/90

=1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90

=9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)

=9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)]

=9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)

=9 – (1 – 1/10) = 9 – 9/10 = 81/10

b)4/3.7 + 4/7.11 + 4/11.15 + 4/15.19 + 4/19.23 + 4/23.27

=4.(4/3.7 + 4/7.11 + ........+ 4/23.27 )

=1.( 1/3.7 + 1/7.11 + ......+ 1/23.27 )

=1.(1/3 - 1/7 + 1/7 - 1/11 +............ + 1/23 - 1/27 )

=1.(1/3 - 1/27 )

=1.(9/27 - 1/27)

=1.8/27

=8/27

c)1/10+1/40+1/88+1/154+1/138+1/340

=1/2.5 + 1/5.8 + 1/11.8 + 1/11.14 + 1/14.17 + 1/17.20

=1/3. (3/2.5  + 3/5.8 + 3/8.11 + 3/11.14 + 3/14.17 + 3/17.20 )

=1/3. ( 1/2 - 1/5 + 1/5 - 1/8 + 1/8 - 1/11 + 1/11 - 1/14 + 1/14 - 1/17 + 1/17 -1/20 )

=1/3. ( 1/2 - 1/20 )

=1/3. 9/20

=3/20

P/S: CHÚC HOK TỐT !

a: \(A=\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+\left(\dfrac{1}{2}\right)^3+...+\left(\dfrac{1}{2}\right)^7\)

=>\(2\cdot A=1+\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2+...+\left(\dfrac{1}{2}\right)^6\)

=>\(2A-A=1-\left(\dfrac{1}{2}\right)^7=1-\dfrac{1}{128}=\dfrac{127}{128}\)

=>\(A=\dfrac{127}{128}\)

b: \(B=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10\cdot11}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}\)

\(=1-\dfrac{1}{11}=\dfrac{10}{11}\)

\(\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)

\(=\dfrac{-1}{4.5}+\dfrac{-1}{5.6}+\dfrac{-1}{6.7}+\dfrac{-1}{7.8}+\dfrac{-1}{8.9}+\dfrac{-1}{9.10}\)

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

\(=\dfrac{-1}{4}-\dfrac{-1}{10}\)

\(=\dfrac{-3}{20}\)

KQ: Số đó là 90 

Hok tốt ^^

Trả lời:

Theo quy luật mk thấy thì : 9=90

Học tốt nhá ~

Là đáp án c.90 nha mọi người

a: 78/42-4/7=13/7-4/7=9/7

100/110-56/88=10/11-7/11=3/11

75/35-11/7+21/49=15/7-11/7+3/7=7/7=1

99/72-15/40-1212/1616=11/8-3/8-3/4=1-3/4=1/4