Phú Nguyễn bạn sai rồi

lay so cuoi cong so dau roi chia 2 nhe

(4/ 3* 9/ 8* 16/ 15* 25/ 24......9801/ 9800)

=(2* 2* 3* 3* 4* 4* 5* 5......*99* 99)/ (1* 3* 2* 4* 3* 5* 4* 6......98* 100)

=((2* 3* 4* 5*......*99)/ (1* 2* 3* 4*....* 98))/ ((2* 3* 4*...99)/ (3* 4* 5*.....*100))

=99* (1/ 50)

=99/ 50

đúng thì k cho mình bn nha (^.^)

\(A=\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{9801}\right)\)

\(=\left(1-\dfrac{1}{2}\right)\left(1+\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1+\dfrac{1}{3}\right)\cdot...\left(1-\dfrac{1}{99}\right)\left(1+\dfrac{1}{99}\right)\)

\(=\left(\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{98}{99}\right)\cdot\left(\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{100}{99}\right)\)

\(=\dfrac{1}{99}\cdot\dfrac{100}{2}=\dfrac{50}{99}\)

Ta thấy khoảng cách của các số lần lượt là : 

8 ; 16 ; 24 và chúng đều chia hết cho 8

Còn lại  tự làm nhé

:))

Ta có 1+9+25+49+...+9801

=1²+3²+5²+7²+...+99²

Ta có công thức tổng quát

1²+3²+5²+...+(2n-1)²=\(\frac{n\left(4n^2-1\right)}{3}\)

Ta có 99=2x50-1

=>1²+3²+5²+...+99²=\(\frac{50.\left(4.50^2-1\right)}{3}=166650\)

\(\dfrac{1}{3}+\dfrac{5}{9}=\dfrac{6}{18}+\dfrac{10}{18}=\dfrac{16}{18}=\dfrac{8}{9}\)

\(\dfrac{1}{7}-\dfrac{1}{9}=\dfrac{9}{63}-\dfrac{7}{63}=\dfrac{2}{63}\)

\(3:\dfrac{5}{9}=3.\dfrac{9}{5}=\dfrac{27}{5}\)

\(3.\dfrac{5}{9}=\dfrac{15}{9}=\dfrac{5}{3}\)

\(\dfrac{1}{9}.\dfrac{9}{3}=\dfrac{1}{3}\)

\(\dfrac{1}{3}:\dfrac{1}{7}=\dfrac{7}{3}\)

\(9+\dfrac{9}{3}=9+3=12\)

\(4-\dfrac{2}{4}=4-\dfrac{1}{2}=\dfrac{7}{2}\)

\(\dfrac{1}{3}\) \(+\) \(\dfrac{5}{9}\) \(=\) \(\dfrac{3}{9}\) \(+\) \(\dfrac{5}{9}\) \(=\) \(\dfrac{3+5}{9}\) \(=\) \(\dfrac{8}{9}\)

\(\dfrac{1}{7}\) \(-\) \(\dfrac{1}{9}\) \(=\) \(\dfrac{9}{63}\) \(-\) \(\dfrac{7}{63}\) \(=\) \(\dfrac{9-7}{63}\) \(=\) \(\dfrac{2}{63}\)

\(\dfrac{1}{9}\) \(\times\) \(\dfrac{9}{3}\) \(=\) \(\dfrac{1\times9}{9\times3}\) \(=\) \(\dfrac{1}{3}\)

\(\dfrac{1}{3}\) \(\div\) \(\dfrac{1}{7}\) \(=\) \(\dfrac{1}{3}\) \(\times\) \(\dfrac{7}{1}\) \(=\) \(\dfrac{1\times7}{3\times1}\) \(=\) \(\dfrac{7}{3}\)

\(3\) \(\div\) \(\dfrac{5}{9}\) \(=\) \(\dfrac{3}{1}\) \(\div\)  \(\dfrac{5}{9}\) \(=\dfrac{3}{1}\times\dfrac{9}{5}=\dfrac{3\times9}{1\times5}=\dfrac{27}{5}\)

\(3\times\dfrac{5}{9}=\dfrac{3}{1}\times\dfrac{5}{9}=\dfrac{3\times5}{1\times9}=\dfrac{5}{3}\)

\(9+\dfrac{9}{3}=\dfrac{9}{1}+\dfrac{9}{3}=\dfrac{27}{3}+\dfrac{9}{3}=\dfrac{27+9}{3}=\dfrac{36}{3}=12\)

\(4\) \(-\dfrac{2}{4}=\dfrac{4}{1}-\dfrac{2}{4}=\dfrac{16}{4}-\dfrac{2}{4}=\dfrac{14}{4}=\dfrac{7}{2}\)

a) \(\dfrac{1}{9}\times\dfrac{4}{7}+\dfrac{1}{9}\times\dfrac{3}{7}=\dfrac{1}{9}\times\left(\dfrac{4}{7}+\dfrac{3}{7}\right)=\dfrac{1}{9}\times1=\dfrac{1}{9}\)

b) \(\dfrac{5}{13}\times\dfrac{189}{18}-\dfrac{5}{13}\times\dfrac{9}{18}=\dfrac{5}{13}\times\left(\dfrac{189}{18}-\dfrac{9}{18}\right)=\dfrac{5}{13}\times\dfrac{180}{18}=\dfrac{5}{13}\times10=\dfrac{50}{13}\)

c) \(\dfrac{12}{7}:\dfrac{4}{9}+\dfrac{4}{7}:\dfrac{4}{9}=\dfrac{12}{7}\times\dfrac{9}{4}+\dfrac{4}{7}\times\dfrac{9}{4}=\left(\dfrac{12}{7}+\dfrac{4}{7}\right)\times\dfrac{9}{4}=\dfrac{16}{7}\times\dfrac{9}{4}=\dfrac{144}{28}=\dfrac{36}{7}\)

cảm ơnnn aaa

a) \(\dfrac{5}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{5}{7}\)

\(=\dfrac{5}{7}\times\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\)

\(=\dfrac{5}{7}\times1\)

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

b) \(\dfrac{1}{10}+\dfrac{5}{9}+\dfrac{4}{9}+\dfrac{9}{10}-1\)

\(=\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\left(\dfrac{1}{10}+\dfrac{9}{10}-1\right)\)

\(=1+0\)

\(=1\)

c) \(\dfrac{5}{7}\times\dfrac{5}{9}+\dfrac{4}{9}\times\dfrac{5}{7}+\dfrac{2}{7}\)

\(=\dfrac{5}{7}\times\left(\dfrac{5}{9}+\dfrac{4}{9}\right)+\dfrac{2}{7}\)

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

\(=1\)

d) \(\dfrac{2}{7}+\dfrac{2}{8}+\dfrac{1}{4}+\dfrac{1}{7}+\dfrac{4}{7}\)

\(=\left(\dfrac{2}{8}+\dfrac{1}{4}\right)+\left(\dfrac{2}{7}+\dfrac{1}{7}+\dfrac{4}{7}\right)\)

\(=\left(\dfrac{1}{4}+\dfrac{1}{4}\right)+1\)

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

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

e) \(\dfrac{4}{5}+\dfrac{3}{10}+\dfrac{2}{10}+0,7\)

\(=\dfrac{4}{5}+\dfrac{5}{10}+\dfrac{7}{10}\)

\(=\dfrac{4}{5}+\dfrac{12}{10}\)

\(=\dfrac{4}{5}+\dfrac{6}{5}\)

\(=\dfrac{10}{5}\)

\(=2\)

g) \(362\times728+326\times272\)

\(=326\times\left(728+272\right)\)

\(=326\times1000\)

\(=326000\)