\(A=1^2+2^2+3^2+....+10^2\\ A=1^{ }+\left(1+1\right)\cdot2+3\cdot\left(2+1\right)+.....+10\cdot\left(9+1\right)\\ A=1+2\cdot1+2+3\cdot2+3+....+10\cdot9+10\\ A=\left(1+2+3...+10\right)+\left(1\cdot2+3\cdot2+.....+10\cdot9\right)\)

Gọi 1+2+3+...+10 là P

Số số hạng là: (10 - 1) : 1 +1 = 10 (số)

P = (10+1) . 10 : 2 = 55 

P = 55

Gọi \(1\cdot2+2\cdot3+....+9\cdot10\)  là C

\(C=1\cdot2+2\cdot3+....+9\cdot10\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot3+....+9\cdot10\cdot3\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+....+9\cdot10\cdot\left(11-8\right)\\ 3\cdot C=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+.....+9\cdot10\cdot11-8\cdot9\cdot10\\ 3\cdot C=9\cdot10\cdot11\\ 3\cdot C=990\\ C=330\)

\(=>A=P+C\\ =>A=55+330\\ A=385\)

b)

\(B=5^2+10^2+15^2+...+50^2\\ B=5^2+\left(2\cdot5\right)^2+\left(3\cdot5\right)^2+....+\left(5\cdot10\right)^2\\ B=5^2+2^2\cdot5^2+3^2\cdot5^2+...+5^2\cdot10^2\\ B=5^2\cdot\left(1+2^2+3^2+....+10^2\right)\\ B=25\cdot\left(1+2^2+3^2+....+10^2\right)\)

\(\left(1+2^2+3^2+....+10^2\right)=A\)

\(=>B=25\cdot A\\ B=25\cdot385\\ B=9625\)

a)

\( 49.(51 - 4) - 51.(49 + 4)\)

\(=49.51-49.4-51.49-51.4\)

\(=49.(51-4-51)-51.4\)

\(=49.(-4)-51.4\)

\(=4.(-49-51)\)

\(=4.(-100)\)

\(=-400\)

b)

\( 71.64 + 32.(-7) - 13.32\)

\(=71.32.2+32.(-7)-13.32\)

\(=142.32+32.(-7)-13.32\)

\(=32.(142-7-13)\)

\(=32.122\)

\(=3904\)

c)

\( 11 + (-13) + 15 + (-17) + ... + 59 + (-61)\)

\(=(-2)+(-2)+...+(-2)\)

\(=(-2).13\)

\(=-26\)

a. 49.51- 49.4 -51.49 -51.4

= -49.4 - 51.4

=4.(-49-51)

=4.-100

=-400

b.71.64 + 32.(-7) -13.32

= 71.64 + 32.(-7-13)

=71.64 + 32.-20 

=71.32.2 +32.-20

=32.(71x2-20)

=32. 122

= 3904

c. (11-13)+(15-17)+..+(59-61)

=-2 x 13

=-26

A. - 279.    B. -170.      C. -4600.      D. -4200

Ta có 1² + 2² + 3² + …10² = 385

Suy ra ( 1² +2² + 3² +…+10² ) .3² = 385.3²

Do đó ta tính được A = 3² + 6² + 9² + …+30²  = 3465

  \(=49\frac{8}{23}-5\frac{7}{32}-14\frac{8}{23}\)

\(=\left(49\frac{8}{23}-14\frac{8}{23}\right)-5\frac{7}{32}\)

\(=35\frac{0}{23}-5\frac{7}{32}\)

\(=\frac{805}{23}-\frac{167}{32}\)

\(\frac{25760}{736}-\frac{3841}{736}\)

\(=\frac{21919}{736}=\frac{953}{32}\)

\(P=\dfrac{32}{64}\cdot\dfrac{-57}{19}+\dfrac{35}{21}\cdot\dfrac{22}{44}=\dfrac{1}{2}\left(-3+\dfrac{5}{3}\right)=\dfrac{1}{2}\cdot\dfrac{-4}{3}=\dfrac{-2}{3}\)

\(Q=\dfrac{75}{125}\cdot\dfrac{82}{164}+\dfrac{49}{98}\cdot\dfrac{-35}{105}=\dfrac{1}{2}\left(\dfrac{3}{5}-\dfrac{1}{3}\right)=\dfrac{1}{2}\cdot\dfrac{4}{15}=\dfrac{2}{15}\)

bài 1 : Tính

2048 : 2³ = 2048 : 8 = 256

bài 1.1 : Tính

625 : 5² . 40 = 625 : 25 . 40 = 25 . 40 = 1000

Bài 2: 

a: \(=3^{11}\)

giúp mk vs nha , mk đang rất cần

\(=49\frac{8}{23}-5\frac{7}{32}-14\frac{8}{23}\)

\(=49\frac{8}{23}-14\frac{8}{23}-5\frac{7}{12}\)

\(=35-5\frac{7}{32}\)

\(=35-\frac{167}{32}\)

\(=\frac{1120}{32}-\frac{167}{32}\)

\(=\frac{935}{32}\)

\(49\frac{8}{23}-\left(5\frac{7}{32}+14\frac{8}{23}\right)\)

\(=49\frac{8}{23}-5\frac{7}{32}-14\frac{8}{23}\)

\(=\left(49\frac{8}{23}-14\frac{8}{23}\right)-5\frac{7}{32}\)

\(=35-5\frac{7}{32}\)

\(=35-\frac{167}{32}\)

\(=\frac{953}{32}\)