Lời giải:

$A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+..+\frac{2}{2017.2019}$

$=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{2019-2017}{2017.2019}$

$=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{2017}-\frac{1}{2019}$

$=1-\frac{1}{2019}=\frac{2018}{2019}$

D = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 + .... + 99 . 100 + 100 . 101

3D=1 . 2 . 3 + 2 . 3 . ( 4 - 1 ) + 3 . 4 . ( 5 - 2 )+ 4 . 5 + ( 6 - 3) + .... + 99. 100 . ( 101 - 98 ) + 100 . 101 . ( 102 - 99 )

3D=1 . 2 . 3+2 . 3 . 4-1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + 4 . 5 . 6 - 3 . 4  . 5 + ..... + 99 . 100 . 101- 98 . 99 . 100 +100 . 101 . 102-99.100.101

3D = 100 . 101 . 102 

D = \(\frac{100.101.102}{3}=343400\)

E = \(2+2^3+2^5+2^7+...+2^{2017}+2^{2019}\)

4E = \(2^3+2^5+2^7+2^9...+2^{2019}+2^{2021}\)

=> 4E - E = \(2^3+2^5+2^7+2^9...+2^{2019}+2^{2021}\)- ( \(2+2^3+2^5+2^7+...+2^{2017}+2^{2019}\))

=> 3E = \(2^{2021}-2\)

=> E = \(\frac{2^{2021}-2}{3}\)

a\()\) 16/9 +3/5

=107/45

b\()\) 4/13--2/17

=51/221--26/221

=77/221

c\()\) -3/2+4/5

=-15/10+8/10

=-7/10

d\()\) 3/-4-1/4

=-1

e\()\) -1/5.5/7

=-1/7

f\()\) 7/8.64/49

=8/7

g\()\) 3/4.15/24

=15/32

`#lv`

`-2/5+(-7/10)-9/6`

`=-2/5-7/10-9/6`

`=-4/10-7/10-9/6`

`=-11/10-3/2`

`=-11/10-15/10`

`=-26/10`

`=-13/5`

__

`1/2+(-2/5)-(-2/3)`

`=1/2-2/5+2/3`

`=5/10-4/10+2/3`

`=1/10+2/3`

`=3/30+20/30`

`=23/30`

__

`5/3-3/4+7/6`

`=20/12-9/12+14/12`

`=11/12+14/12`

`=25/12`

__

`-1/5+5/3-3/2`

`=-3/15+25/15-3/2`

`=22/15-3/2`

`=44/30-45/30`

`=-1/30`

__

`1/4-7/8+(-9/10)`

`=2/8-7/8-9/10`

`=-5/8-9/10`

`=-25/40-36/40`

`=-61/40`

__

`5/4+1/2+(-7/12)`

`=15/12+6/12-7/12`

`=21/12-7/12`

`=14/12`

`=7/6`

__

`-5/8-1/3+(-7/6)`

`=-5/8-1/3-7/6`

`=-15/24-8/24-28/24`

`=-52/24`

`=-13/6`

__

`-3/4-7/10+(-5/6)`

`=-3/4-7/10-5/6`

`=-45/60-42/60-50/60`

`=-137/60`

Bài làm

a, (-2/5) + (-7/10) - 9/6 =(-12/30) + (-21/30) - 45/30=(-33/30) - 45/30 = (-78/30)

b,1/2 + (-2/5) - (-2/3) = 15/30 + (-12/30) - (-20/30) = 3/30 - (-20/30) = 23/30

c,5/3 - 3/4 + 7/6 = 40/24 - 18/24 + 28/24 = 22/24 + 28/24 = 50/24 = 25/12

d, (-1/5) + 5/3 - 3/2 = (-6/30) + 50/30 - 45/30 = 44/30 - 45/30 = (-1/30)

e, 1/4 - 7/8 + (-9/10) = 10/40 - 35/40 - 36/40 = (-25/40) - 36/40 = (-61/40)

f, 5/4 +1/2 + (-7/12) = 15/12 + 6/12 - 7/12 = 21/12 - 7/12 = 14/12 = 7/6

g,(-5/8) -1/3 + (-7/6) = (-15/24) - 8/24 - 28/24 = (-23/24) - 28/24 = (-51/24) 

k,(-3/4) - 7/10 + (-5/6) = (-45/60) - 42/60 - 50/60 = (-87/60) - 50/60 = (-137/60)

chúc bn học tốt nha

sai thì mn góp ý giúp mk

a; - \(\dfrac{4}{11}\) + \(\dfrac{5}{6}\) + \(\dfrac{7}{11}\) - \(\dfrac{5}{6}\)

= (-\(\dfrac{4}{11}\) + \(\dfrac{7}{11}\)) + (\(\dfrac{5}{6}\)  - \(\dfrac{5}{6}\))

= - \(\dfrac{3}{11}\) + 0

= - \(\dfrac{3}{11}\)

b; -\(\dfrac{5}{6}\).\(\dfrac{7}{13}\) + \(\dfrac{19}{13}\).\(\dfrac{6}{-5}\) + \(\dfrac{2}{5}\)

= - \(\dfrac{35}{78}\) - \(\dfrac{114}{65}\) + \(\dfrac{2}{5}\)

= - \(\dfrac{859}{390}\) + \(\dfrac{2}{5}\)

= - \(\dfrac{703}{390}\)

c; \(\dfrac{3}{7}\).(-0,5 + \(\dfrac{3}{2}\)) -\(\dfrac{2}{7}\) : 25%)

= \(\dfrac{3}{7}\).1 - \(\dfrac{8}{7}\)

= \(-\dfrac{5}{7}\)