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7 tháng 6 2018

làm dài lắm,nếu muốn thì k minh còn ko thì thôi

7 tháng 6 2018

a,0,36.350+1,2.20.3+9.4.4,5

=13.3.35+12.2.3+9.2.3.3

=3.(13.35+12.2+.9.2.3)

=3.(455+24+54)

=3.533

=1599

b,2015.2016-5/2015.2015+2010

=4062240-5+2010

=4064245

c,2/1.3+2/3.5+2/5.7+...+2/71.73

=1-1/3+1/3-1/5+1/5-1/7+...+1/71-1/73

=1-1/73

=72/73

d,(1+1/2).(1+1/3)+...+(1+1/2018)

=3/2.4/3.5/4+...+2019/2018

=2019/2

e,E=1/4.5+1/5.6+1/6.7+...+1/80.81(làm tương tự với phần d nên mình làm ngắn

     =1/4-1/81

     =77/324

f,F=3/2.3+3/3.4+...+3/99.100

=3.(1/2.3+1/3.4+...+1/99.100)(làm tương tự với d

=3.(1/2-1/100)

=3.49/100

=147/100

gG=5/1.4+5/4.7+...+5/61.64

3G=5.(3/1.4+3./4.7+...+3/61.64)

     =5.(1-1/64)

     =5.63/64

     =315/64

ok nha bạn,mình giữ đúng lời hứa.

7 tháng 6 2016

a) 1/5.6 + 1/6.7 + 1/7.8 + ... + 1/24.25

= 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + ... + 1/24 - 1/25

= 1/5 - 1/25

= 4/25

b) 2/1.3 + 2/3.5 + 2/5.7 + ... + 2/99.101

= 1 - 1/3 + 1/3 - 1/5 + 1/5 - 1/7 + ... + 1/99 -1/101

= 1 - 1/101

= 100/101

c) 3/1.4 + 3/4.7 + ... + 3/2002.2005

= 1 - 1/4 + 1/4 - 1/7 + ... + 1/2002 - 1/2005

= 1 - 1/2005

= 2004/2005

d) 5/2.7 + 5/7.12 + ... + 5/1997.2002

= 1/2 - 1/7 + 1/7 - 1/12 + ... + 1/1997 - 1/2002

= 1/2 - 1/2002

= 500/1001

7 tháng 6 2016

a,A =  \(\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+...+\frac{1}{24\times25}\)

A\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{24}-\frac{1}{25}\)

A\(=\frac{1}{5}-\frac{1}{25}=\frac{5}{25}-\frac{1}{25}=\frac{4}{25}\)

b, B=\(\frac{2}{1\times3}+\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{99\times101}\)

B= \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

B=\(1-\frac{1}{101}=\frac{100}{101}\)

c, \(C=\frac{3}{1\times4}+\frac{3}{4\times7}+...+\frac{3}{2002\times2005}\)

C= \(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{2002}-\frac{1}{2005}\)

C= \(1-\frac{1}{2005}=\frac{2004}{2005}\)

d, D= \(\frac{5}{2\times7}+\frac{5}{7\times12}+...+\frac{5}{1997\times2002}\)

D= \(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{12}+...+\frac{1}{1997}-\frac{1}{2002}\)

D= \(\frac{1}{2}-\frac{1}{2002}=\frac{1001}{2002}-\frac{1}{2002}=\frac{1000}{2002}=\frac{500}{1001}\)

8 tháng 6 2018

\(D=\left(1+\frac{1}{2}\right).\left(1+\frac{1}{3}\right).\left(1+\frac{1}{4}\right)...+\left(1+\frac{1}{2018}\right)\)

     \(=\frac{3}{2}.\frac{4}{3}......\frac{2018}{2017}.\frac{2019}{2018}\)

      \(=\frac{3.4.5....2018.2019}{2.3.4.5....2017.2018}=\frac{2019}{2}\)

\(E=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{79.80}+\frac{1}{80.81}\)

      \(=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+....+\frac{1}{80}-\frac{1}{81}\)

        \(=\frac{1}{4}-\frac{1}{81}\)

          \(=\frac{77}{324}\)

8 tháng 6 2018

\(\text{D}=\left(1+\frac{1}{2}\right)\cdot\left(1+\frac{1}{3}\right)\cdot...\cdot\left(1+\frac{1}{2017}\right)\cdot\left(1+\frac{1}{2018}\right)\)

\(\text{D}=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdot...\cdot\frac{2018}{2017}\cdot\frac{2019}{2018}\)

\(\text{D}=\frac{2019}{2}\)

\(\text{E}=\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{79.80}+\frac{1}{80.81}\)

\(\text{E}=\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{79}-\frac{1}{80}+\frac{1}{80}-\frac{1}{81}\)

\(\text{E}=\frac{1}{4}-\frac{1}{81}=\frac{81}{324}-\frac{4}{324}=\frac{77}{324}\)

3 tháng 7

c; 17\(\dfrac{2}{31}\) - (\(\dfrac{15}{17}\) + 6\(\dfrac{2}{31}\))

= 17 + \(\dfrac{2}{31}\) - \(\dfrac{15}{17}\) - 6 - \(\dfrac{2}{31}\)

= (17 - 6)  - \(\dfrac{15}{17}\) + (\(\dfrac{2}{31}\) - \(\dfrac{2}{31}\))

= 11  - \(\dfrac{15}{17}\)+ 0

=    \(\dfrac{172}{17}\)

3 tháng 7

b; 130\(\dfrac{25}{28}\) + 120\(\dfrac{17}{35}\)

= 130 + \(\dfrac{25}{28}\) + 120 + \(\dfrac{17}{35}\)

= (130 + 120) + (\(\dfrac{25}{28}\) + \(\dfrac{17}{35}\))

= 250 + (\(\dfrac{125}{140}\) + \(\dfrac{68}{140}\))

= 250 +  \(\dfrac{193}{140}\)

= 250\(\dfrac{193}{140}\)

8 tháng 6 2018

f,F=3. (1/2 .3 + 1/3.4 +...+ 1/99.100)

    = 3. (1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +...+ 1/99 - 1/100

    = 3. (1/2 - 1/100)

    = 3. 49/100

    = 147/100

g, G = 5/3. (3/1.4 + 3/4.7 +...+ 3/61.64)

        = 5/3 . (1 - 1/4 + 1/4 - 1/7 +...+ 1/61 - 164

        = 5/3 . (1-1/64)

        = 5/3 . 63/64

        = 105/64

8 tháng 6 2018

f,    \(F=\frac{3}{2.3}+\frac{3}{3.4}+...+\frac{3}{99.100}\)

\(\Leftrightarrow F=3\left(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\right)\)

\(\Leftrightarrow F=3\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\right)\)

\(\Leftrightarrow F=3\left(\frac{1}{2}-\frac{1}{100}\right)\)

\(\Leftrightarrow F=3\left(\frac{49}{100}\right)=\frac{147}{100}\)

g,    \(G=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{61.64}\)

\(\Leftrightarrow G=5\left(\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{61.64}\right)\)

\(\Leftrightarrow G=5.\frac{1}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{61}-\frac{1}{64}\right)\)

\(\Leftrightarrow G=\frac{5}{3}\left(1-\frac{1}{64}\right)\)

\(\Leftrightarrow G=\frac{5}{3}.\frac{63}{64}=\frac{105}{64}\)

8 tháng 6 2018

\(G=\frac{5}{1.4}+\frac{5}{4.7}+...+\frac{5}{61.64}\)

\(\Rightarrow G=\frac{5}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+..+\frac{3}{61.64}\right)\)

\(\Rightarrow G=\frac{5}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+..+\frac{1}{61}-\frac{1}{64}\right)\)

\(\Rightarrow G=\frac{5}{3}.\left(1-\frac{1}{64}\right)=\frac{5}{3}.\frac{63}{64}\)

\(\Rightarrow G=\frac{5.63}{3.64}=\frac{5.21.3}{3.64}=\frac{5.21}{64}=\frac{105}{64}\)

3 tháng 8 2018

A =  1 + 2 + 3 + ... + 2018 (có 2018 số )

   = (2018 + 1) . 2018 : 2 = 2037171

B = 1 + 3 + 5 + ... + 2017(có  1009 số )

   = (2017 + 1) . 1009 : 2 = 1018081

C = 2 + 4 + 6 + ... + 2018 (Có 1009 số )

   = (2018 + 2) x 1009 : 2 = 1019090

D = 72 . 153 + 27.153 + 153

    = (72 + 27 + 1) . 153

    = 100 . 153 = 15300

12 tháng 7 2015

A, 1/4.5 + 1/5.6 + 1/6.7+ 1/7.8 

= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 

= 1/4 - 1/8 

=1/8 

B; 3/1.4 + 3/4.7 + 3/7.10 = 1/1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10

 = 1- 1/10 

= 9/10

C, 1/1.3 + 1/3.5 + 1/5.7 + .. +1/2007.2009 

= 1/2 ( 2/1.3 + 2/3.5 + ... + 2/2007.2009)

= 1/2 ( 1/1 - 1/3 + 1/3 - 1/5 + ... +1/2007 - 1/2009)

= 1/2 ( 1- 1/2009)

= 1/2 . 2008/2009

= 1004/2009

D; 8/2.6 + 8/6.10 + 8/10.14 + 8/14.18 + 8/18.22

= 2( 4/2.6 + 4/6.10 + .. +4/18.22)

= 2 ( 1/2 - 1/6 + 1/6 - 1/10 + .. + 1/18 - 1/22)

= 2 ( 1/2 - 1/22)

 = 2 .5/11

= 10/11

E; 3/2.4 + 3/4.6 + ... +3/998.1000

 = 3/2( 2/2.4 + 2/4.6 +.. +2/998.1000)

= 3/2 .( 1/2 - 1/4 + 1/4 - 1/6 + ... +1/998 - 1/1000 )

=3/2 . 449/1000

= 1497/2000

ẤN đúng cho mình nha làm xong đứt hơi 

12 tháng 7 2015

a )  1/4.5 + 1/5.6 + 1/6.7+ 1/7.8 

= 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 

= 1/4 - 1/8 

=1/8 

b )  3/1.4 + 3/4.7 + 3/7.10 = 1/1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10

 = 1- 1/10 

= 9/10

c )  1/1.3 + 1/3.5 + 1/5.7 + .. +1/2007.2009 

= 1/2 ( 2/1.3 + 2/3.5 + ... + 2/2007.2009)

= 1/2 ( 1/1 - 1/3 + 1/3 - 1/5 + ... +1/2007 - 1/2009)

= 1/2 ( 1- 1/2009)

= 1/2 . 2008/2009

= 1004/2009

d )  8/2.6 + 8/6.10 + 8/10.14 + 8/14.18 + 8/18.22

= 2( 4/2.6 + 4/6.10 + .. +4/18.22)

= 2 ( 1/2 - 1/6 + 1/6 - 1/10 + .. + 1/18 - 1/22)

= 2 ( 1/2 - 1/22)

 = 2 .5/11

= 10/11

e )  3/2.4 + 3/4.6 + ... +3/998.1000

 = 3/2( 2/2.4 + 2/4.6 +.. +2/998.1000)

= 3/2 .( 1/2 - 1/4 + 1/4 - 1/6 + ... +1/998 - 1/1000 )

=3/2 . 449/1000

= 1497/2000

30 tháng 6 2018

a) ( 1/2-1/3-1/6).(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10

0.(1/2+2/3+3/4+...+2017/2018) + 3/4.x = 9/10

0+3/4.x = 9/10

3/4.x = 9/10

x = 9/10: 3/4

x = 6/5

b) x + ( 3/1.3+3/3.5+...+3/13.15) = 11/5

x + 3/2. ( 1-1/3 + 1/3 - 1/5 + ...+ 1/13 - 1/15) = 11/5

x + 3/2. ( 1-1/15) = 11/5

x + 3/2.14/15 = 11/5

x + 7/5 = 11/5

x = 11/5 - 7/5

x = 4/5

30 tháng 6 2018

..... là gì?