a) \(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}+\frac{71}{72}+\frac{89}{90}\)

\(=1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+1-\frac{1}{30}+1-\frac{1}{42}+1-\frac{1}{56}+1-\frac{1}{72}+1-\frac{1}{90}\)

\(=8-\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

\(=8-\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\right)\)

\(=8-\left(\frac{3-2}{2.3}+\frac{4-3}{3.4}+\frac{5-4}{4.5}+\frac{6-5}{5.6}+\frac{7-6}{6.7}+\frac{8-7}{7.8}+\frac{9-8}{8.9}+\frac{10-9}{9.10}\right)\)

\(=8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\right)\)

\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)=7,6\)

b) Bạn làm tương tự. 

mnbvcxzasdf

976554

2:

A=-(1/4-1/5+1/5-1/6+...+1/9-1/10)

=-(1/4-1/10)

=-1/4+1/10

=-5/20+2/20=-3/20

a) \(19.43+\left(-20\right).43-\left(-40\right)\)

\(=43.\left(19-20\right)+40\)

\(=-43+40\)

\(=-3\)

b) \(6^7:6^5+3.3^2-2021^0\)

\(=6^2+3^3-1\)

\(=36+27-1\)

\(=62\)

c) \(465+\left[\left(-38\right)+\left(-465\right)\right]-\left[12-\left(-42\right)\right]\)

\(=465-38+\left(-465\right)-12-42\)

\(=-92\)

1 + 2 + 3 + ... + n = n(n + 1)/2

1 + 3 + 5 + 7 + ... + 2n − 1 = n²

2 + 4 + 6 + 8 + ... + 2n = n(n + 1)

\(-9-\left(-129\right)+\left(-119\right)-301+12\)

\(=120+\left(-420\right)+12\)

\(=-300+12\)

\(=-288\)

Chúc bạn học tốt

-9-(-129)+(-119)-301+12

= -9+129+(-119)-301+12

= 120-119-301+12

= 1-301+12

= -300+12

= -288

  -9-(-129) + (-119) - 301 + 12

= -9 + 129 + (-119) - 301 + 12

= 120 + (-119) - 301 + 12

= 1 - 301 + 12

= -300 + 12

= -288

^^ Học tốt =)

127.(27 - 56) - 27.(127 - 56)

= 127.27 - 127.56 - 27.127 + 27.56

= (127.27 - 27.127) - (127.56 - 27.56)

= 0 - 56(127 - 27)

= 0 - 56.100

= 0 - 5600

= -5600

127.(27-56)- 27 . (127 - 56)

\(=\left(127-127\right)\cdot\left(27-27\right)\cdot\left(56-56\right)\)

\(=0\cdot0\cdot0\)

\(=0\)

cach giai rui mk tich cho

\(27.332+93.43+57.61+69.57\\ =27.332+93.43+57.\left(61+69\right)\\ =27.332+93.43+57.130\\ =8964+3999+7410=20373\\ 34.75+75.66-65.100\\ =\left(34+66\right).75-65.100\\ =100.75-65.100\\ =100.\left(75-65\right)\\ =100.10=1000\\ \left(456.11+912\right).37:13:74\\ =5928:13:\left(74:37\right)\\ =456:2=228\\ 6^2:4.3+2.5^2\\ =36:4.3+2.25\\ =9.3+50=27+50=77\\ 5.4^2-18:3^2\\ =5.16-18:9\\ =80-2=78\\\left[\left(315+372\right).3+\left(372+315\right).7\right]:\left(26.13+74.14\right)\\ =687.\left(3+7\right):\left(338+1036\right)\\ 687.10:1374\\ =6870:1374=5\\ 12:\left\{390:\left[500-\left(125+35.7\right)\right]\right\}\\ =12:\left[390:\left(500-370\right)\right]\\ =12:\left(390:130\right)=12:3=4\\ 192000-\left(1500.2+1800.3+1800.2:3\right)\\ =192000-\left(3000+5400+1200\right)\\ =192000-9600=182400\)

\(\frac{5}{4}+\frac{7}{12}+\frac{7}{5}+\frac{75}{100}+\frac{40}{25}+\frac{20}{48}\)

\(=\frac{5}{4}+\frac{7}{12}+\frac{7}{5}+\frac{3}{4}+\frac{8}{5}+\frac{5}{12}\)

\(=\left(\frac{5}{4}+\frac{3}{4}\right)+\left(\frac{7}{12}+\frac{5}{12}\right)+\left(\frac{7}{5}+\frac{8}{5}\right)\)

\(=\frac{8}{4}+\frac{12}{12}+\frac{15}{5}\)

\(=2+1+3\)

\(=6\)

Đặt A=5/4 + 7/12 + 7/5 + 75/100 + 40/25 + 20/48

=>A=125/100 + 28/48 + 35/25 + 75/100 + 40/25 + 20/48

=>A=(125/100 + 75/100) + (28/48 + 20/48) + (35/25 + 40/25)

=>A=        2                     +            1             +           3

=>A=                    6

Vậy A=6