Question

[Đỗ Khánh Vy]

Câu 3.Tính 

 

 

Câu trả lời của bạn

 

 

Câu4.Tính *

 

 

Answer 1

[Nguyễn Minh Quang]

Câu 3

\(A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+..+\frac{1}{10.11}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+..+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}=\frac{9}{22}\)

câu 4

\(B=\frac{1}{2}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+..+\frac{1}{99}-\frac{1}{101}\right)=\frac{1}{2}\left(\frac{1}{11}-\frac{1}{101}\right)=\frac{45}{1111}\)

Answer 2

[Mỹ Châu]

Câu 3

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+...+\frac{1}{90}+\frac{1}{110}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+...+\frac{1}{9.10}+\frac{1}{10.11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}\)

\(=\frac{9}{22}\)

Câu 4

\(\frac{1}{11.13}+\frac{1}{13.15}+\frac{1}{15.17}+...+\frac{1}{97.99}+\frac{1}{99.101}\)

\(=2\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{97}-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\right)\)

\(=2\left(\frac{1}{11}-\frac{1}{101}\right)\)

\(=2.\frac{90}{1111}\)

\(=\frac{180}{1111}\)