Em nên gõ công thức trực quan để đề bài rõ ràng nhé

a)\(=\dfrac{16}{13}-\dfrac{3}{15}+\dfrac{6}{13}=\dfrac{22}{13}-\dfrac{3}{15}=\dfrac{96}{65}\)

b)\(=\dfrac{21}{8}-\left(\dfrac{5}{10}+\dfrac{6}{10}\right)=\dfrac{21}{8}-\dfrac{11}{10}=\dfrac{61}{40}\)

c)\(=\dfrac{27}{10}-3-\dfrac{4}{7}--\dfrac{61}{70}\)

d)\(=\dfrac{576}{702}=\dfrac{4}{5}\)

e)\(=\left(\dfrac{20}{15}-\dfrac{12}{15}\right)\times\dfrac{25}{2}=\dfrac{8}{15}\times\dfrac{25}{2}=\dfrac{20}{3}\)

f)\(=\dfrac{24}{12}-\dfrac{4}{12}-\dfrac{6}{12}-\dfrac{2}{12}-\dfrac{3}{12}=\dfrac{9}{12}=\dfrac{3}{4}\)

d) \(=\dfrac{32}{45}x\dfrac{18}{16}=\dfrac{576}{720}=\dfrac{115}{114}\)

e) \(=\left(\dfrac{4}{3}-\dfrac{4}{5}\right)x\dfrac{25}{12}=\dfrac{8}{15}x\dfrac{25}{12}=\dfrac{200}{180}=\dfrac{10}{9}\)

f) \(=\dfrac{2}{1}-\dfrac{1}{3}-\dfrac{1}{2}-\dfrac{1}{6}-\dfrac{3}{12}=\dfrac{24}{12}-\dfrac{4}{12}-\dfrac{6}{12}-\dfrac{2}{12}-\dfrac{3}{12}\)

\(=\dfrac{20}{12}-\dfrac{4}{12}-\dfrac{3}{12}=\dfrac{16}{12}-\dfrac{3}{12}=\dfrac{13}{12}\)

x:1/2 = (2/3.3/4).4/5.15/8

x:1/2 = 6/12.60/40

x:1/2 = 1/2.3/2

x:1/2 = 3/4

x      = 3/4.1/2

x      = 3/8

(. là nhân nhé mik đánh máy sách tay nên ko có dấu nhân k mk nhé)

cam on ban

kick đúng mk vs

\(A=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+....+\frac{1}{120}\)

Ta có :

\(\frac{1}{10}< 1\)

\(\frac{1}{15}< 1\)

\(\frac{1}{21}< 1\)

........................

\(\frac{1}{120}< 1\)

\(\Rightarrow\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+...+\frac{1}{120}< 1\)

\(\Rightarrow A< 1\)( đpcm)

Ta có : A =  \(\frac{1}{10}+\frac{1}{15}+...+\frac{1}{120}\)

= \(\frac{1}{20}\times2+\frac{1}{30}\times2+...+\frac{1}{240}\times2\)

= \(2\times\left(\frac{1}{20}+\frac{1}{30}+...+\frac{1}{240}\right)\)

= \(2\times\left(\frac{1}{4\times5}+\frac{1}{5\times6}+...+\frac{1}{15\times16}\right)\)

= \(2\times\left(\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{15}-\frac{1}{16}\right)\)

= \(2\times\left(\frac{1}{4}-\frac{1}{16}\right)\)

= \(2\times\frac{3}{16}\)

= \(\frac{3}{8}\)< 1 

=> A < 1 

A < 1 nhe ban

a) \(\frac{1}{2.9}+\frac{1}{9.7}+\frac{1}{7.19}+...+\frac{1}{202.509}=\frac{2}{4.9}+\frac{2}{9.14}+\frac{2}{14.19}+...+\frac{2}{504.509}\)

\(=\frac{2}{5}\left(\frac{5}{4.9}+\frac{5}{9.14}+\frac{5}{14.19}+...+\frac{5}{504.509}\right)\)

\(=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+...+\frac{1}{504}-\frac{1}{509}\right)=\frac{2}{5}\left(\frac{1}{4}-\frac{1}{509}\right)\)

\(=\frac{2}{5}.\frac{505}{2036}=\frac{101}{1018}\)

b) \(\frac{1}{10.9}+\frac{1}{18.13}+...+\frac{1}{802.405}=\frac{2}{10.18}+\frac{2}{18.26}+...+\frac{2}{802.810}\)

\(=\frac{2}{8}\left(\frac{8}{10.18}+\frac{8}{18.26}+...+\frac{8}{802.810}\right)=\frac{1}{4}\left(\frac{1}{10}-\frac{1}{18}+\frac{1}{18}-\frac{1}{26}+...+\frac{1}{802}-\frac{1}{810}\right)\)

\(=\frac{1}{4}\left(\frac{1}{10}-\frac{1}{810}\right)=\frac{1}{4}.\frac{40}{405}=\frac{10}{405}\)

Bạn vào câu hỏi tương tự tham khảo !