67.12 + 67.89 - 67

= 67.(12 + 89 - 1)

= 67.100

= 6700

$67\cdot12+67\cdot89-67$

$=67\cdot(12+89-1)$

$=67\cdot(101-1)$

$=67\cdot100$

$=6700$

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

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)

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

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

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

hello bạn lớp mấy vậy???

=(1-2)+(3-4)+...+(51-52)+53

= -1 + -1 + ... + -1 + 53

= -1 x (52:2)+53

= -26 + 53

=27

= (1-2)+(3-4)+...+(51-52)+53

= (-1) + (-1) + (-1) + ... + (-1) + 53

= -1 x (52 : 2) + 53

= -26 + 53

=27 nhớ tích and kết bạn

19 x ( 52 + 38 ) - 9 x ( 52 + 38 )

= 19 x 90 - 9 x 90

= ( 19 - 9 ) x 90

= 10 x 90

= 900

\(\dfrac{2}{5}:\dfrac{3}{7}\times\dfrac{3}{7}:\dfrac{2}{5}+2019=\left(\dfrac{2}{5}:\dfrac{2}{5}\right)\times\left(\dfrac{3}{7}:\dfrac{3}{7}\right)+2019=1\times1+2019=1+2019=2020\)

a)Dãy trên có số số hạng là:

(51-1):2+1=26(số hạng)

Tổng trên là:

(51+1)x26:2=676.

b)Dãy trên có số số hạng là:

(52-2):2+1=26(số hạng)

Tổng trên là:

(52+2)x26:2=702.

c)Tổng trên là:

(100+2)x[(100-2):2+1]:2=2550.

Chúc em học tốt^^

1 + 3 + 5 + ... + 51

= ( 51 + 1 ) x 26 : 2 = 676

2 + 4 + 6 + ... + 52

= ( 52 + 2 ) x 26 : 2 = 702

2 + 4 + 6 + ... + 100

= ( 100 + 2 ) x 50 : 2 = 2550

x=8 nên x+1=9

\(F=x^{13}-9x^{12}+9x^{11}-9x^{10}+...-9x^2+9x-2\)

\(=x^{13}-x^{12}\left(x+1\right)+x^{11}\left(x+1\right)-x^{10}\left(x+1\right)+...-x^2\left(x+1\right)+x\left(x+1\right)-2\)

\(=x^{13}-x^{13}-x^{12}+x^{12}+...-x^3-x^2+x^2+x-2\)

=x-2

=8-2

=6

\(\left(1-\dfrac{5}{17}\right)\left(\dfrac{3}{8}-\dfrac{5^2}{24}\right)\)

\(=\dfrac{17-5}{17}\cdot\dfrac{9-25}{24}\)

\(=\dfrac{12}{17}\cdot\dfrac{-16}{24}=\dfrac{-16}{17}\cdot\dfrac{12}{24}=\dfrac{-16}{17}\cdot\dfrac{1}{2}=-\dfrac{8}{17}\)

a, \(\dfrac{90}{37}-\dfrac{38}{25}-\dfrac{8}{25}-\dfrac{4}{25}\)

= \(\dfrac{90}{37}\) - \(\dfrac{38+8+4}{25}\)

= \(\dfrac{90}{37}\) - 2

= \(\dfrac{16}{37}\)

\(\dfrac{24}{29}\) + \(\dfrac{32}{41}\) + \(\dfrac{34}{29}\) + \(\dfrac{50}{41}\)

=(\(\dfrac{24}{29}\) + \(\dfrac{34}{29}\)) + (\(\dfrac{32}{41}\) + \(\dfrac{50}{41}\))

= \(\dfrac{58}{29}\) + \(\dfrac{82}{41}\)

= 2 + 2

= 4

c, \(\dfrac{73}{24}\) - \(\dfrac{22}{29}\) - \(\dfrac{25}{24}\) + \(\dfrac{51}{29}\)

= ( \(\dfrac{73}{24}\) - \(\dfrac{25}{24}\)) +( \(\dfrac{51}{29}\) - \(\dfrac{22}{29}\))

= \(\dfrac{48}{24}\) + \(\dfrac{29}{29}\)

= 2 + 1

= 3