A= -5/1/7+32/5=0.22857142857142286

B= -2/1/3-1/2/7=119047619047619

a=2001000

b=2500

c=1156

a = 2001000

b = 2500

c =1156

a. 1 + 2 + 3 +....+ 1999 + 2000

    Số trung gian là : (2000 + 1) : 2 = 1000,5

    Số hạng là : (2000 - 1) : 1 + 1 = 2000

     Tổng dãy trên là : 1000,5 x 2000 = 2001000

b. 1 + 3 + 5 + 7 +....+ 99

      Số trung gian là :  ( 99 + 1 ) : 2 = 50

      Số hạng là :  (99 - 1 ) : 2 + 1 = 50

      Tổng dãy trên là :  50 x 50 = 2500

c. 1 + 5 + 10 + 15 +...+ 105 = 1 + ( 5 + 10 + 15 + ....+ 105 )

       Số trung gian là :  ( 105 + 5 ) : 2 = 55

       Số hạng là :  ( 105 - 5 ) : 5 + 1 = 21

       Tổng dãy trên là :  1 + ( 55 x 21 ) = 1156

1) 1/3 x 1/2 x 3/7 = 3/42 = 1/14

2) 5/4 x 1/3 +1/7 = 5/12 + 1/7 = 35/84 + 12/84 = 47/84

3) 8 x ( 8/9 - 2/3 ) = 8 x 2/9 = 16/9

4) 5/6 x 48/20 x 1/2 = 240/240 = 1

5) ( 2/5 + 3/4 ) + 8 = 23/20 + 8 = 23//20 + 160/20 = 183/20

6) 10 x ( 1/2 - 1/5 ) = 10 x 3/10 = 10/1 x 3/10 = 30/10 = 3

\(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right).\left(1+\frac{1}{5}\right).\left(1+\frac{1}{6}\right).\left(1+\frac{1}{7}\right)\)

\(=\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.\frac{6}{5}.\frac{7}{6}.\frac{8}{7}\)

\(=\frac{3.4.5.6.7.8}{2.3.4.5.6.7}\)

\(=\frac{8}{2}\)

\(=4\)

a) \(\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right).\left(1+\frac{1}{5}\right).\left(1+\frac{1}{6}\right).\left(1+\frac{1}{7}\right)\)

= \(\frac{3}{2}.\frac{4}{3}.\frac{5}{4}.\frac{6}{5}.\frac{7}{6}.\frac{8}{7}\)

= \(\frac{3.4.5.6.7.8}{2.3.4.5.6.7}\)

= \(4\)

1/3+1/6+1/10+...+2/[x.(x+1)]= 2011/2013
12(13+16+...1x(x+1)=2011201312(13+16+...1x(x+1)=20112013
12.3+13.4+14.5+...+1x(x+1)=2011201312.3+13.4+14.5+...+1x(x+1)=20112013
12−13+13−14+...+1x−1x+1=2011201312−13+13−14+...+1x−1x+1=20112013 
12−1x+1=2011201312−1x+1=20112013 
1x+1=12−201120131x+1=12−20112013 
1x+1=−200940261x+1=−20094026 
(x+1).−2009=4026(x+1).−2009=4026 
−2009x+(−2009)=4026−2009x+(−2009)=4026 
−2009x=4026−(−2009)−2009x=4026−(−2009) 
−2009x=6035−2009x=6035 
x=−60352009

\(A=1+2+2^2+2^3+...+2^{90}\\ A=1+\left(2+2^2+2^3+2^4+2^5+2^6\right)+...+\left(2^{85}+2^{86}+2^{87}+2^{88}+2^{89}+2^{90}\right)\\ A=1+2\left(1+2+2^2+2^3+2^4+2^5\right)+...+2^{85}\left(1+2+2^2+2^3+2^4+2^5\right)\\ A=1+2\cdot63+...+2^{85}\cdot63\\ A=1+21\left(2\cdot3+2^2\cdot3+...+2^{85}\cdot3\right):21.dư.1\)

a)\(\left(x+3\right)\times5+1=20\Leftrightarrow5x+15=19\)

\(\Leftrightarrow5x=4\Leftrightarrow x=\frac{4}{5}\)

b)sai đề

c)\(2\frac{3}{7}\times x+1\frac{5}{4}=5\frac{3}{42}\)\(\Leftrightarrow\frac{17}{7}\times x+\frac{9}{4}=\frac{71}{14}\) \(\Leftrightarrow\frac{17}{7}\times x+\frac{63}{28}=\frac{142}{28}\)

\(\Leftrightarrow\frac{17}{7}\times x=\frac{79}{28}\Leftrightarrow x=\frac{17}{7}:\frac{79}{28}\) \(\Leftrightarrow x=\frac{17}{7}\times\frac{28}{79}\Leftrightarrow x=\frac{476}{553}=\frac{68}{79}\)

d)\(10\frac{2}{3}-x:\frac{6}{7}=8\frac{1}{3}-6\frac{2}{7}\Leftrightarrow\frac{32}{3}-x:\frac{6}{7}=\frac{25}{3}-\frac{44}{7}\) \(\Leftrightarrow\frac{224}{21}-x:\frac{6}{7}=\frac{75}{21}-\frac{132}{21}\Leftrightarrow-\frac{57}{21}-\frac{224}{21}\)

\(\Leftrightarrow-x:\frac{6}{7}=-\frac{281}{21}\Leftrightarrow-x=-\frac{281}{21}\times\frac{6}{7}\) \(\Leftrightarrow-x=-\frac{1686}{147}\Leftrightarrow x=\frac{562}{49}=11\frac{23}{49}\)

1: \(=\dfrac{1}{3}\cdot\dfrac{3}{7}\cdot\dfrac{1}{2}=\dfrac{1}{7\cdot2}=\dfrac{1}{14}\)

2: =5/12+1/7

=35/84+12/84=47/84

3: =8(8/9-6/9)

=8*2/9=16/9

4: \(=\dfrac{5}{12}\cdot\dfrac{12}{5}=1\)

5: =16/5+6

=16/5+30/5=46/5

6: =10*1/2-10*1/5

=5-2=3