\(\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{8}\right)-\frac{1}{4}\times\frac{1}{2}\)

\(=\frac{2}{3}\times\frac{3}{4}\times\frac{4}{5}\times\frac{5}{6}\times\frac{6}{7}\times\frac{7}{8}-\frac{1}{4}\times\frac{1}{2}\)

\(=\frac{2}{8}-\frac{1}{4}\times\frac{1}{2}\)

\(=\frac{2}{8}-\frac{1}{8}=\frac{1}{8}\)

d

Ta có:

 \(\left(1-\frac{1}{11}\right)\times\left(1-\frac{1}{10}\right)\times\left(1-\frac{1}{9}\right)\times\left(1-\frac{1}{8}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{6}\right)\)

\(=\frac{10}{11}\times\frac{9}{10}\times\frac{8}{9}\times\frac{7}{8}\times\frac{6}{7}\times\frac{5}{6}\)

\(=\frac{10\times9\times8\times7\times6\times5}{11\times10\times9\times8\times7\times6}\)

\(=\frac{5}{11}\)

cho mk một tk đi bà con ơi

ủng hộ mk đi làm ơn

\(a,\frac{5\cdot84\cdot105}{35\cdot50\cdot21}=\frac{1\cdot4\cdot3}{1\cdot10\cdot1}=\frac{1\cdot2\cdot3}{1\cdot5\cdot1}=\frac{6}{5}\)

\(b,\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)...\left(1-\frac{1}{8}\right)\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{7}{8}\)

\(=\frac{1}{8}\)

a)

\(\frac{5\cdot84\cdot105}{35\cdot50\cdot21}\)

\(=\frac{5\cdot7\cdot2\cdot6\cdot35\cdot3}{35\cdot5\cdot10\cdot3\cdot7}\)

\(=\frac{6}{5}\)

Mình làm luôn ko chép lại đề nhé

= ( \(\frac{1}{3}+\frac{3}{3}\)) x ( \(\frac{1}{4}+\frac{4}{4}\)) x ... x ( \(\frac{1}{16}+\frac{16}{16}\))

= \(\frac{4}{3}x\frac{5}{4}x...x\frac{17}{16}\)

= \(\frac{4x5x6x...x17}{3x4x5x...x16}\)

= \(\frac{17}{3}\)

Ta có 4/3x5/4x6/5x...x17/16 rút gọn ta được 17/3

(1 - 1/5) x (1 - 1/6) x (1 - 1/7) x (1 - 1/8) =

= 4/5 x 5/6 x 6/7 x 7/8 =

= (2/1 x 1/3) x (3/1 x 1/4) =

=2/3 x 3/4 =

= 6/12 = 1/2

(1-1/5 ) *(1- 1/7 ) * (1- 1/7) *(1- 1/8)

=4/5* 5/6* 6/7* 7/8

=1/2

( 1+1/2) : (1+1/3) : (1+1/4)

=3/2 : 4/3 : 3/4

=3/2 x 3/4 x4/3

=3/2 x 1= 3/2 

(1-1/2)×(1-1/3)×(1-1/4 )×...×(1-1/2006)×(1-1/2007)

=(2/2-1/2)×(3/3-1/3)×(4/4-1/4)×..×(2006/2006-1/2006)×(2007/2007-1/2007)

=1/2×2/3×3/4×..×2005/2006×2006/2007

=1/2007

ta có : A=1/2+1/4+..+1/1024

=> A=1/2¹+1/2²+..+1/2¹⁰

=> A.2=(1/2¹+1/2²+..+1/2¹⁰).2

=> A.2=1+1/2¹+1/2²+..+1/2⁹

=> 2A-A=(1+1/2¹+1/2²+..+1/2⁹)-(1/2¹+1/2²+..+1/2¹⁰)

=> A=1-1/2¹⁰

\(\frac{2174}{1024}\)