\(\dfrac{2}{3}\)

=\(\left(\dfrac{5}{17}+\dfrac{12}{17}\right)+\left(\dfrac{1}{22}-\dfrac{23}{22}\right)+\dfrac{2}{3}\)

=\(\dfrac{17}{17}-\dfrac{22}{22}+\dfrac{2}{3}\)

=\(1-1+\dfrac{2}{3}\)

=0+\(\dfrac{2}{3}\)

=\(\dfrac{2}{3}\)

a: \(17\cdot85+15\cdot17-120\)

\(=17\left(85+15\right)-120\)

=1700-120

=1580

b: \(2^3\cdot17-2^3\cdot14\)

\(=2^3\left(17-14\right)\)

\(=8\cdot3=24\)

c: \(20-\left\lbrack30-\frac{\left(5-1\right)^2}{2}\right\rbrack\)

\(=20-30+\frac{4^2}{2}\)

\(=-10+\frac{16}{2}=-10+8=-2\)

d: \(80-\left(4\cdot5^2-3\cdot2^2\right)\)

\(=80-\left(4\cdot25-3\cdot4\right)\)

=80-100+12

=92-100

=-8

e: \(27\cdot77+24\cdot27-27\)

\(=27\left(77+24-1\right)\)

\(=27\cdot100=2700\)

f: \(174:\left\lbrace2\cdot\left\lbrack36+\left(4^2-23\right)\right\rbrack\right\rbrace\)

\(=\frac{174}{2\cdot\left(36+16-23\right)}=\frac{87}{52-23}=\frac{87}{29}=3\)

a) \(3.5^2+15.2^2-26\div2\)

= 3.25 + 15.4 - 13

= 75 + 60 - 13

= 135 - 13

= 122

b) \(5^3.2-100\div4+2^3.5\)

= 125.2 - 25 + 8.5

= 250 - 25 + 40

= 225 + 40

= 265

c)\(6^2\div9+50.2-3^3.33\)

= 36 : 9 + 100 - 9.33

= 4 + 100 - 297

= 104 - 297

= -193

d)\(3^2.5+2^3.10-81\div3\)

= 9.5 + 8.10 - 27

= 45 + 80 - 27

= 125 - 27

= 98

e) \(5^{13}\div5^{10}-25.2^2\)

= 5³ - 25.4

= 125 - 100

= 25

f) \(20\div2^2+5^9\div5^8\)

= 20 : 4 + 5

= 5 + 5

= 10

Nguyễn Quang Thành trả lời cụ thể đi

1/

Tổng A là tổng các số hạng cách đều nhau 4 đơn vị.

Số số hạng: $(101-1):4+1=26$

$A=(101+1)\times 26:2=1326$

2/

$B=(1+2+2^2)+(2^3+2^4+2^5)+(2^6+2^7+2^8)+(2^9+2^{10}+2^{11})$

$=(1+2+2^2)+2^3(1+2+2^2)+2^6(1+2+2^2)+2^9(1+2+2^2)$

$=(1+2+2^2)(1+2^3+2^6+2^9)$

$=7(1+2^3+2^6+2^9)\vdots 7$