\(=\frac{4.4}{3.5}.\frac{5.5}{4.6}......\frac{20.20}{19.21}\)

\(=\left(\frac{4.5...20}{3.4....19}\right).\left(\frac{4.5...20}{5.6....21}\right)\)

\(=\frac{20}{3}.\frac{4}{21}\)

\(=\frac{80}{63}\)

\(=\frac{4.4}{3.5}.\frac{5.5}{4.6}.....\frac{20.20}{19.21}\)

=\(\left(\frac{4.5...20}{3.4...19}\right).\left(\frac{4.5.....20}{5.6....21}\right)\)

=\(\frac{20}{3}.\frac{4}{21}\)=\(\frac{80}{63}\)

hok tốt

\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)

\(=\frac{2}{3\times5}+\frac{2}{5\times7}+\frac{2}{7\times9}+...+\frac{2}{19\times21}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

\(=\frac{1}{3}-\frac{1}{21}\)

\(=\frac{7}{21}-\frac{1}{21}\)

\(=\frac{6}{21}\)

Rút gọn kết quả là \(\frac{2}{7}\), k mk nha mk trả lời đầu tiên đó

\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+....+\frac{2}{399}\)

\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{19}-\frac{1}{21}\)

\(=\frac{1}{3}-\frac{1}{21}\)

\(=\frac{6}{21}=\frac{2}{7}\)

ta có 

A=\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)

\(=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+....+\frac{2}{19.21}\)

\(=2\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)\)

\(=2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\)

\(=2\left(\frac{1}{3}-\frac{1}{21}\right)\)

=\(\frac{4}{7}\)

\(A=\)\(\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{19.21}\)\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{19}-\frac{1}{21}=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)

Ta có: \(G=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)

\(y=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

\(=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)

mình thắc mắc quy luật của phép tính trên là gì : 15 -> 35 -> 63 ... -> 399 ?

Quy luật la cac so o duoi mau cach nhau 2 don vi ( cach nhau mot so bang tu):

2/15=2/3.5 ( 3 va 5 cach nhau 2don vi)

2/35=2/5.7 ( 5 va 7 cach nhau 2 don vi)

.........

(Cai nay minh gui cho ban Duy Thanh nhe!!!!!!!!!!!!!!!!!!!)

\(=1+\frac{1}{3}+1+\frac{1}{15}+...+1+\frac{1}{399}.\)

\(=10+\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)

=\(10+\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\right)\)

=\(10+\frac{1}{2}\left(1-\frac{1}{21}\right)=10+\frac{1}{2}.\frac{20}{21}=\frac{220}{21}\)

Thanh you

\(A=\frac{2}{15}+\frac{2}{35}+\frac{2}{63}+...+\frac{2}{399}\)

=>\(A=\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{19.21}\)

=>\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\)

=>\(A=\frac{1}{3}-\frac{1}{21}\)

=>\(A=\frac{2}{7}\)

\(\frac{2}{7}\)

\(=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}\)

\(=\frac{1}{3}-\frac{1}{21}=\frac{2}{7}\)

chi tiết đc hơn ko bạn