\(B=1+2+2^2+...+2^{19}\)

\(2B=2+2^2+2^3+...+2^{20}\)

\(2B-B=B=2^{20}-1\)

B chia 7 dư 3

tách B thành :

B = 1 + 2( 1 + 2 + 2^2 ) +2^2(1 + 2 + 2^2 ) + ... + 2^17(1 + 2 + 2 ^ 2 )

B = 1 + 2.7 + 2^2.7 + .... + 2^17.7

B = 7( 2 + 2^2 + ... + 2^17 ) + 1 = 7k + 1 ( k là số tự nhiên )

Vậy B chia 7 dư 1

B = 3 + 2^2 + 2^3 + 2^4 ...+2^19

= 3 + 2^2( 1+ 2 + 2^2 + 2^3 + 2^4...+2^17)

= 3+ 2^2. 3 + 2^2 .( 2^2 +2^3 + ...+ 2^17)

= 3 + 2^2 . 3 + 2^4 . 3 +.....+2^18 . 3

=3( 1+2^2 + 2^4 + 2^6 +....+ 2^18) => chia hết cho 3

=3(2^3-7 + 2^3-4 + 2^4+2^6 + ...+2^18)

=3(2^3 + 2^3 -1-1-9 +2^3.2^1 + 2^3.2^2 +..+2^3.2^15  + 15-15)

=3(2^3-1)(1 + 1 +2^1 + 2^2 +...+2^15) + 18

Chia cho 7 dư 4

   2/7 + 3/5

= 10/35 + 21/35  

= 31/35

   31/35 - 2/7  

= 31/35 - 10/35  

= 21/35

= 3/5

   31/35 - 2/5

= 31/35 - 14/35  

= 17/35

   3/5 + 2/7  

= 21/35 + 10/35

= 31/35

2/7 + 3/5 = 10/35 + 21/35 = 31/35

31/35 - 2/7 = 31/35 - 10/35 = 21/35

31/35 - 2/5 = 31/35 - 21/35 = 10/35

3/5 + 2/7 = 21/35 + 10/35 = 31/35

2/7+3/5 =31/35

31/35-2/7=21/35

31/35-2/5=17/35

3/5+2/7=31/35

nhớ tích cho minh nhé mình kb cho mình là con gái

4: \(=\dfrac{2+3}{7}+\dfrac{1+6}{9}-\dfrac{5}{6}=\dfrac{5}{7}+\dfrac{7}{9}-\dfrac{5}{6}=\dfrac{83}{126}\)

5: \(=\dfrac{-5-2}{7}+\dfrac{3+1}{4}-\dfrac{1}{5}=-\dfrac{1}{5}\)

6: \(=\dfrac{-3-28}{31}+\dfrac{-6-1}{17}+\dfrac{1-5}{25}=-1-\dfrac{7}{17}-\dfrac{4}{25}=-\dfrac{668}{425}\)

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

\(=\left(\dfrac{2}{7}+\dfrac{3}{7}\right)+\left(\dfrac{1}{9}+\dfrac{5}{9}\right)+\dfrac{-5}{6}\)

\(=\dfrac{5}{7}+\dfrac{2}{3}+\dfrac{-5}{6}\)

\(=\dfrac{30+28+\left(-35\right)}{42}=\dfrac{23}{42}\)
 

5. \(\dfrac{-5}{7}+\dfrac{3}{4}+\dfrac{-1}{5}+\dfrac{-2}{7}+\dfrac{1}{4}\)

\(=\left(\dfrac{-5}{7}+\dfrac{-2}{7}\right)+\left(\dfrac{3}{4}+\dfrac{1}{4}\right)+\dfrac{-1}{5}\)

\(=\dfrac{-7}{7}+\dfrac{4}{4}+\dfrac{-1}{5}\)

\(=-1+1+\dfrac{-1}{5}\)

\(=-\dfrac{1}{5}\)
 

6. \(\dfrac{-3}{31}+\dfrac{-6}{17}+\dfrac{1}{25}+\dfrac{-28}{31}+\dfrac{-1}{17}+\dfrac{-1}{5}\)

\(=\left(\dfrac{-3}{31}+\dfrac{-28}{31}\right)+\left(\dfrac{-6}{17}+\dfrac{-1}{17}\right)+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=\dfrac{-31}{31}+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=-1+\dfrac{-7}{17}+\dfrac{1}{25}+\dfrac{-1}{5}\)

\(=\dfrac{-425+\left(-175\right)+17+\left(-85\right)}{425}=\dfrac{-668}{425}\)

Mik cần nhanh, mai mik hok r T^T

1) Tính nhanh 

\(A=\frac{4}{7}+\frac{3}{4}+\frac{2}{7}+\frac{5}{4}+\frac{1}{7}\)

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

\(=1+2=3\)

Ghép tương tự vs B 

A = \(\frac{4}{7}+\frac{3}{4}+\frac{2}{7}+\frac{5}{4}+\frac{1}{7}\)

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

   =           \(1+2\)

   =            \(3\)

a: =7/8:(2/9-18+1/36)-5/12

=-7/142-5/12=-397/852

b: =3/7(4/9+5/9:6/12)=2/3

c: =5^8(16/31-47/31)+1/3=-5^8+1/3

d: =7/2(3/8+5/8:4/15)=609/64

Giúp tớ với tớ cần gấp

a: \(=\dfrac{-5}{7}-\dfrac{2}{7}+\dfrac{3}{4}+\dfrac{1}{4}-\dfrac{1}{5}=-\dfrac{1}{5}\)

b: \(=\dfrac{-3}{31}-\dfrac{28}{31}+\dfrac{-6}{17}-\dfrac{11}{17}+\dfrac{1}{29}-\dfrac{1}{5}=\dfrac{-24}{145}\)