A có (2007-3):3+1=669(số hạng)                                                                                                                      A= (2007+3)x669:2=1003500

Số cá số hạng : ( 2007 - 3 ) : 3 + 1 = 669 ( số hạng )

Tổng dãy số trên là : ( 2007 + 3 ) . 669 : 2 = 672345

ĐS : 672345

Dãy số trên có số số hạng là :

    ( 2007 - 3 ) : 3 + 1 = 669 ( số hạng )

Tổng của A là :

    ( 2007 + 3 ) x 669 : 2 = 672345

         Đáp số : 672345 .

a)= 2021.2021-2020.(2021+1)
  = 2021.(2020+1)-2020.(2021+1)
  = (2021.2020)+2021-(2020.2021)-2020
  = 1

b) B= (1+2-3-4)+(5+6-7-8)+(9+10-11-12)...........+(2017+2018-2019-2020)+2021
    B= -4+(-4)+....................(-4)+2021
    B= -4x505+2021
    B= -2020 + 2021
    B = 1

\(=20.\left(-9\right)+\left(-20\right).21\)

\(=-180+\left(-420\right)\)

\(=-600\)

a) =20.(-9)+(-20).21

=20.(-9)+20.(-21)

=20[(-9)+(-21)]

=20.(-30)

=-600

Cách 1: Theo kiểu dài                       |           Cách 2:Ngắn gọn
a) (29 – 9). (-9) + (-13 – 7). 21          |       a) (29-9) . (-9) + (-13-7) . 21
= 20. (-9) + [- (13 + 7). 21]                 |       =20.(-9)+(-20).21
= 20. (-9) + (-20). 21                          |       =180+(-420)
= (-20). 9 + (-20). 21                          |       =600
= (-20). (9 + 21)                                 |
= (-20). 30                                          |
= - (20. 30)                                         |
= - 600.                                              |

(Chúc bạn học tốt nha~!)

b: \(=128\left(-25-89+89-125\right)=128\cdot\left(-150\right)=-19200\)

a)

(-12)(-13)+13(-22) = 12.13 - 13.22 = 13(12-22)=13.(-10)=-130

b) 15(-14) +15(-6) + (-20).25 = 15[(-14)+(-6)]+(-20).25=15.(-20)+(-20).25=(-20)(15+25)=-20.40=-800

c) -65.(87-17)-87(17-65) = 

a)(-12).(-13)+13.(-22)=12.13+13.(-22)=13.[12+(-22)]=13.(-10)=-130

b)15.(-14)+15.(-6)+(-20).25=15.[(-14)+(-6)]+(-20).25=15.(-20)+(-20).25=(-20).(15+25)=(-20).40=-800

c)-65.(87-17)-87.(17-65)=-65.87-(-65).17-87.17+87.65

=-65.87+65.17-87.17+87.65

=[(-65)+65].87+(65-87).17

=0.87+(-22).17

=0+(-374)=-374

a: \(A=21\cdot100-11\cdot100+90\cdot100+100\cdot125\cdot16\)

\(=100\left(21-11+90\right)+100\cdot2000\)

\(=100\left(10+90+2000\right)=2100\cdot100=210000\)

b: \(=\dfrac{5\cdot2^{30}\cdot3^{18}-2^{29}\cdot3^{20}}{5\cdot2^{28}\cdot3^{19}-7\cdot2^{29}\cdot3^{18}}\)

\(=\dfrac{2^{29}\cdot3^{18}\left(5\cdot2-3^2\right)}{2^{28}\cdot3^{18}\left(5\cdot3-7\cdot2\right)}=2\)

a) 145 + 43 + (-145) + 57

= [145 + (-145)] + [43 + 57]

= 0 + 100

= 100

A) = (145+(-145))+(43+57)

= 0 + 100

= 100

Bài 2: Tính một cách hợp lý:

a) 145 + 43 + (– 145) + 57;

= 145 - 145 + 43 + 57 = 0 + 100 = 100

b) (– 213) + 36 + (– 787) + 64;

= -213 - 787 + 36 + 64 = -1000 + 100 = -900

c) (– 2) + (– 4) + (– 6) + (– 10) + 8 + 10 + 12;

= -2 +12 - 4 - 6 - 10 + 10 + 8 = 10 - 10 -10 + 10 + 8 = 8 

d) (– 2 020) + (– 598) + (– 201) + 498 + 301.

= -2020 - 799 + 799 = -2020

a: \(\left(-\dfrac{5}{6}+\dfrac{2}{5}\right):\dfrac{3}{8}+\left(\dfrac{4}{5}-\dfrac{11}{30}\right):\dfrac{3}{8}\)

\(=\left(-\dfrac{5}{6}+\dfrac{2}{5}\right)\cdot\dfrac{8}{3}+\left(\dfrac{4}{5}-\dfrac{11}{30}\right)\cdot\dfrac{8}{3}\)

\(=\dfrac{8}{3}\left(-\dfrac{5}{6}+\dfrac{2}{5}+\dfrac{4}{5}-\dfrac{11}{30}\right)\)

\(=\dfrac{8}{3}\cdot\dfrac{-25+36-11}{30}\)

=0

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

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

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

\(=\dfrac{7}{3}\cdot0=0\)

c: \(\dfrac{-13}{18}\cdot\dfrac{5}{8}+\dfrac{-5}{18}\cdot\dfrac{2}{9}+\dfrac{-13}{18}\cdot\dfrac{3}{8}+\dfrac{-5}{18}\cdot\dfrac{7}{9}\)

\(=\left(-\dfrac{13}{18}\cdot\dfrac{5}{8}+\dfrac{-13}{18}\cdot\dfrac{3}{8}\right)+\left(-\dfrac{5}{18}\cdot\dfrac{2}{9}+\dfrac{-5}{18}\cdot\dfrac{7}{9}\right)\)

\(=-\dfrac{13}{18}\left(\dfrac{5}{8}+\dfrac{3}{8}\right)+\dfrac{-5}{18}\left(\dfrac{2}{9}+\dfrac{7}{9}\right)\)

\(=-\dfrac{13}{18}-\dfrac{5}{18}=-\dfrac{18}{18}=-1\)

d: Sửa đề: \(\dfrac{-11}{19}\cdot\dfrac{4}{9}+\dfrac{-8}{19}\cdot\dfrac{3}{7}+\dfrac{-11}{19}\cdot\dfrac{5}{9}+\dfrac{-8}{19}\cdot\dfrac{4}{7}\)

\(=\left(-\dfrac{11}{19}\cdot\dfrac{4}{9}+\dfrac{-11}{19}\cdot\dfrac{5}{9}\right)+\left(\dfrac{-8}{19}\cdot\dfrac{3}{7}+\dfrac{-8}{19}\cdot\dfrac{4}{7}\right)\)

\(=-\dfrac{11}{19}\left(\dfrac{4}{9}+\dfrac{5}{9}\right)+\dfrac{-8}{19}\left(\dfrac{3}{7}+\dfrac{4}{7}\right)\)

\(=-\dfrac{11}{19}-\dfrac{8}{19}=-\dfrac{19}{19}=-1\)

\(a.\left(-\dfrac{5}{6}+\dfrac{2}{5}\right):\dfrac{3}{8}+\left(\dfrac{4}{5}-\dfrac{11}{30}\right):\dfrac{3}{8}\)

\(=\left(-\dfrac{13}{30}\right):\dfrac{3}{8}+\dfrac{13}{30}:\dfrac{3}{8}\)

\(=\left[\left(-\dfrac{13}{30}+\dfrac{13}{30}\right)\right]:\dfrac{3}{8}\)

\(=0:\dfrac{3}{8}=0\)

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

\(=\left(-\dfrac{7}{20}\right):\dfrac{3}{7}+\dfrac{7}{20}:\dfrac{3}{7}\)

\(=\left[\left(-\dfrac{7}{20}+\dfrac{7}{20}\right)\right]:\dfrac{3}{7}=0:\dfrac{3}{7}=0\)

\(c.-\dfrac{13}{18}.\dfrac{5}{8}+-\dfrac{5}{18}.\dfrac{2}{9}+-\dfrac{13}{18}.\dfrac{3}{8}+-\dfrac{5}{18}.\dfrac{7}{9}\)

\(=\left(\dfrac{5}{8}+\dfrac{3}{8}\right).-\dfrac{13}{18}+\left(\dfrac{2}{9}+\dfrac{7}{9}\right).-\dfrac{5}{18}\)

\(=1.-\dfrac{13}{18}+1.-\dfrac{5}{18}=-\dfrac{13}{18}+-\dfrac{5}{18}=-1\)

\(d.-\dfrac{11}{19}.\dfrac{4}{9}+\dfrac{-8}{19}.\dfrac{3}{7}+-\dfrac{11}{19}.\dfrac{5}{9}+-\dfrac{9}{19}.\dfrac{4}{7}\)

\(=\left(\dfrac{4}{9}+\dfrac{5}{9}\right).-\dfrac{11}{19}+-\dfrac{24}{133}+-\dfrac{36}{133}\)

\(=-\dfrac{11}{19}+-\dfrac{60}{133}=-\dfrac{137}{133}\)

\(a,\dfrac{11}{22}-\dfrac{3}{16}.\dfrac{8}{18}+\dfrac{1}{18}=\dfrac{1}{2}-\dfrac{1}{12}+\dfrac{1}{18}=\dfrac{18}{36}-\dfrac{3}{36}+\dfrac{2}{36}=\dfrac{17}{36}\)

\(b,\dfrac{5}{7}+\dfrac{3}{7}:4-\dfrac{8}{9}.\dfrac{-3}{4}=\dfrac{5}{7}+\dfrac{3}{7}.\dfrac{1}{4}-\dfrac{-2}{3}=\dfrac{5}{7}+\dfrac{3}{28}+\dfrac{2}{3}=\dfrac{60}{84}+\dfrac{9}{84}+\dfrac{56}{84}=\dfrac{125}{84}\)