\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{110}\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+...+\frac{1}{10\cdot11}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\)

\(=1-\frac{1}{11}=\frac{10}{11}\)

Đặt\(S=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{42}...+\frac{1}{110}\)

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{10.11}\)

\(S=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{10}-\frac{1}{11}\)

\(S=1-\frac{1}{11}\)

\(S=\frac{11}{11}-\frac{1}{11}=\frac{10}{11}\)

\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{561}\)

\(A=\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{1122}\)

\(A=\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+...+\frac{2}{33.34}\)

\(A=2.\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{33.34}\right)\)

\(A=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{33}-\frac{1}{34}\right)\)

\(A=2.\left(\frac{1}{2}-\frac{1}{34}\right)\)

\(A=2.\left(\frac{17-1}{34}\right)\)

\(A=2.\frac{8}{17}\)

\(A=\frac{16}{17}>\frac{16}{18}=\frac{8}{9}\)

\(\Rightarrow A>\frac{8}{9}\)

\(A=1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-\frac{1}{2^4}-...-\frac{1}{2^{10}}\)

\(2A=2-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^9}\)

\(2A+A=\left(2-1-\frac{1}{2}-\frac{1}{2^2}-...-\frac{1}{2^9}\right)+\left(1-\frac{1}{2}-\frac{1}{2^2}-\frac{1}{2^3}-\frac{1}{2^{10}}\right)\)

\(3A=2-\frac{1}{2^{10}}\)

\(3A=\frac{2^{11}-1}{2^{10}}\)

\(A=\frac{2^{11}-1}{2^{10}.3}\)

II.Dùng các cụm từ gợi ý để hoàn thành những câu sau.Em thay đổi trật tự từ nếu cần thiết:

1.Small/thin/sister/white/and/his/lips/teeth/has.

=>His sister has small white teeth and thin lips.

2.part/cooking/Sunday/Linda/in/this/a/taking/competition/is.

=>Linda is taking part in a cooking competition this Sunday.

3.John/usually/sports/free time/sometimes/camp/classmate.

=>John usually plays sports in his free time, but sometimes he goes camping with his classmate.

C1:What is the distance to go to Great Wall of China                                                                                 

1. How long is the Great Wall of China ?

=> What is the length of the Great Wall of China.

2. How heavy are you ?

=> How much kilos of you ?

3. Hung is 1.60 meters tall. Ba is 1.50 meters tall.

=> Ba is 10 kilos...

4. How often do Ba and Lan go to the zoo a month ?

=> How many time do Ba and Lan go to the zoo a month ?