=\(\dfrac{\left(\dfrac{7}{2^9}-\dfrac{14}{2^{11}}+\dfrac{21}{768}\right)^2}{\left(\dfrac{5}{2^9}-\dfrac{20}{2^{12}}+\dfrac{25}{1280}\right)^2}\)

= \(\dfrac{\left[7.\left(\dfrac{1}{2^9}-\dfrac{2}{2^{11}}+\dfrac{3}{768}\right)\right]^2}{\left[5.\left(\dfrac{1}{2^9}-\dfrac{4}{2^{12}}+\dfrac{5}{1280}\right)\right]^2}\)

=\(\dfrac{7^2}{5^2}\)

a) (2/5 x 25/29) + (3/5 x 25/29)
= (50/145) + (75/145)
= 125/145

b) (5/2 x 3/7) - (3/14 : 6/7)
= 15/14 - (3/14 x 7/6)
= 15/14 - 1/2
= (30/28) - (14/28)
= 16/28
= 4/7

c) (15/4 : 5/12) - (6/5 : 11/15)
= (15/4 x 12/5) - (6/5 x 15/11)
= 180/20 - 90/55
= 9 - 18/11
= (99/11) - (18/11)
= 81/11
= 7 4/11

a) (2/3) + (20/21 x 3/2 x 7/5)
= 2/3 + (60/210)
= 2/3 + 2/7
= (14/21) + (6/21)
= 20/21

b) (5/17 x 21/32 x 47/24 x 0)
= 0

c) (11/3 x 26/7) - (26/7 x 8/3)
= (286/21) - (208/21)
= 78/21
= 3 9/21
= 3 3/7

a) (25/8) : x = 5/16
=> (25/8) x (16/5) = x
=> 4 = x

b) x + (7/15) = 6/15
=> x = (6/15) - (7/15)
=> x = -1/15

c) x : (28/49) = 7/12
=> x x (49/28) = 7/12
=> x = (7/12) x (28/49)
=> x = 1/2

a) 6 x x = (5/8) : (3/4)
=> 6x = (5/8) x (4/3)
=> 6x = 20/24
=> 6x = 5/6
=> x = (5/6) / 6
=> x = 5/36

câu,b,không,đủ,thông,tin,nhan,bạn.

49/25

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/

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

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

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

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

3/
$C=1+2+2^2+2^3+...+2^{99}$

$2C=2+2^2+2^3+2^4+...+2^{100}$

$\Rightarrow 2C-C=2^{100}-1$

$\Rightarrow C=2^{100}-1$

\(F=\left(\dfrac{A}{B}\right)^2\)

\(A=\left(\dfrac{7}{2^9}-\dfrac{14}{2^{11}}+\dfrac{21}{768}\right)=\left(\dfrac{7}{2^9}-\dfrac{14}{2^{11}}+\dfrac{7}{256}\right)=\left(\dfrac{7}{2^9}-\dfrac{7}{2^{10}}+\dfrac{7}{2^8}\right)=7.\left(\dfrac{1}{2^9}-\dfrac{1}{2^{10}}+\dfrac{1}{2^8}\right)\)

\(B=\left(\dfrac{5}{2^9}-\dfrac{20}{2^{12}}+\dfrac{25}{1280}\right)=\left(\dfrac{5}{2^9}-\dfrac{4.5}{2^{12}}+\dfrac{5}{256}\right)=\left(\dfrac{5}{2^9}-\dfrac{5}{2^{10}}+\dfrac{5}{2^8}\right)=5.\left(\dfrac{1}{2^9}-\dfrac{1}{2^{10}}+\dfrac{1}{2^8}\right)\)\(F=\left(\dfrac{A}{B}\right)^2=\left(\dfrac{7}{5}\right)^2\)

làm được câu a thui

\(\frac{1}{100}=\frac{1}{10.10}\);\(\frac{1}{90}=\frac{1}{9.10}\);...

Suy ra \(\frac{1}{10.10}-\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-\frac{1}{6.7}-...-\frac{1}{1.2}\)

\(\frac{1}{10}-\frac{1}{10}-\frac{1}{10}-\frac{1}{9}-...-1-\frac{1}{2}\)

\(\frac{1}{10}-\frac{1}{2}\)

\(-\frac{4}{10}\)

Thanks bạn nha

sai rồi đừng chép

a: \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}\)

\(=4-\sqrt{15}+\sqrt{15}=4\)

b: \(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

\(=2+\sqrt{3}-2+\sqrt{3}\)

\(=2\sqrt{3}\)

c: \(\sqrt{29+12\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

\(=\sqrt{\left(2\sqrt{5}+3\right)^2}-\sqrt{\left(2\sqrt{5}-3\right)^2}\)

\(=2\sqrt{5}+3-2\sqrt{5}+3=6\)

M = 7 .9 + 14. 27 + 21 . 36 / 21 . 29 + 42 . 81 + 63 . 108 = 7 . 9 (1 + 2.3 + 3.4) / 21( 29 + 2 . 81 + 3 . 108) = 3 . 19 / 29 + 3⁴ . (2 + 2²) = 3 . 19 / 29 + 3⁴ . 6 = 57 / 515

a) \(\frac{12\cdot13}{5\cdot24}=\frac{13}{5\cdot2}=\frac{13}{10}\)

b)\(\frac{25\cdot17+25\cdot12}{29\cdot13+29\cdot14}=\frac{25\cdot\left(17+12\right)}{29\left(13+14\right)}=\frac{25\cdot29}{29\cdot27}=\frac{25}{27}\)

a, \(\frac{12.13}{5.24}=\frac{12.13}{5.2.12}=\frac{13}{10}\)

b, \(\frac{25.17+25.12}{29.13+29.14}=\frac{25.\left(17+12\right)}{29.\left(13+14\right)}=\frac{25.29}{29.27}=\frac{25}{27}\)

a, \(\frac{12.13}{5.24}=\frac{12.13}{5.12.2}=\frac{13}{5.2}=\frac{13}{10}\)

b, \(\frac{25.17+25.12}{29.13+29.14}=\frac{25\left(17+12\right)}{29\left(13+14\right)}=\frac{25.29}{29.27}=\frac{25}{27}\)