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

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

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

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

d

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

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

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

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

a)

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

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

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

b) 1/3+1/3^2+1/3^3+1/3^4+1/3^5 (goi tong bang M)

3M=1+1/3+1/3^2+1/3^3+1/3^4

3M-M=1-1/3^5

2M=242/243

M=242/243*1/2=121/243

^ là gì vậy 

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

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

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

Tính nhanh: 

\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\)\(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}+\frac{1}{9}\)

\(=\left(\frac{1}{1}+\frac{1}{9}\right)+\left(\frac{1}{2}+\frac{1}{8}\right)\)\(+\left(\frac{1}{3}+\frac{1}{7}\right)+\left(\frac{1}{4}+\frac{1}{6}\right)+\frac{1}{5}\)

\(=\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{5}\)

\(=\frac{4}{10}+\frac{2}{5}=\frac{2}{5}+\frac{1}{5}=\frac{3}{5}\)

tks giúp mk nha! cảm ơn nhiều ạ...

Đặt \(A=2-1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

\(=2-\frac{1}{9}=\frac{18}{9}-\frac{1}{9}=\frac{17}{9}\)

1    \(A=\left(1+\frac{1}{2}\right)\times\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{4}\right)\times.........\times\left(1+\frac{1}{2016}\right)\times\left(1+\frac{1}{2017}\right)\)

\(A=\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times......\times\frac{2016}{2017}\times\frac{2018}{2017}\)

\(A=\frac{2018}{2}=1009\)

\(B=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.......+\frac{2}{43.45}\)

\(B=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-......+\frac{1}{43}-\frac{1}{45}\)

\(B=\frac{1}{3}-\frac{1}{45}\)

\(B=\frac{14}{45}\)

2     \(\frac{2017}{2018}\times\frac{23}{47}+\frac{24}{2018}\times\frac{2017}{47}\)

\(=\frac{2017}{2018}\times\frac{23}{47}+\frac{24}{47}\times\frac{2017}{2018}\)

\(=\frac{2017}{2018}\times\left(\frac{23}{47}+\frac{24}{47}\right)\)

\(=\frac{2017}{2018}\times1\)

=\(\frac{2017}{2018}\)

bạn nào xem giải thế có đúng ko