Question

làm giúp mình bài này nhék

\(A=\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-.....-\frac{1}{2.3}-\frac{1}{1.2}\)

Mình cảm ơn nhiều mình sẽ ****

Answer 1

Answer 2

bị nhầm xíu sửa lại

\(\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-...-\frac{1}{2.3}-\frac{1}{1.2}=\frac{1}{9}-\frac{1}{10}-\frac{1}{8}+\frac{1}{9}-\frac{1}{7}+\frac{1}{8}-...-\frac{1}{2}+\frac{1}{3}-\frac{1}{1}+\frac{1}{2}\)

\(=\frac{2}{9}-\frac{1}{10}-\frac{1}{1}=\frac{20}{90}-\frac{9}{90}-\frac{90}{90}=-\frac{79}{90}\)

Answer 3

Ta có: \(A=\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-...-\frac{1}{2.3}-\frac{1}{1.2}\)

\(\Rightarrow A=\left(\frac{1}{9}-\frac{1}{10}\right)-\left(\frac{1}{8}-\frac{1}{9}\right)-\left(\frac{1}{7}-\frac{1}{8}\right)-...-\left(\frac{1}{2}-\frac{1}{3}\right)-\left(1-\frac{1}{2}\right)\)

\(\Rightarrow A=\frac{1}{9}-\frac{1}{10}-\frac{1}{8}+\frac{1}{9}-\frac{1}{7}+\frac{1}{8}-...-\frac{1}{2}+\frac{1}{3}-1+\frac{1}{2}\)

\(\Rightarrow A=\frac{1}{9}-\frac{1}{10}+\frac{1}{9}-1\)

\(\Rightarrow A=\left(\frac{1}{9}+\frac{1}{9}\right)-\left(\frac{1}{10}+1\right)\)

\(\Rightarrow A=\frac{2}{9}-\frac{11}{10}\)

\(\Rightarrow A=\frac{20}{90}-\frac{99}{90}\)

\(\Rightarrow A=-\frac{79}{90}\)

Vậy \(A=-\frac{79}{90}\)

Chúc bạn hok tốt nah! 

Answer 4

Answer 5

\(\frac{1}{9.10}-\frac{1}{8.9}-\frac{1}{7.8}-...-\frac{1}{2.3}-\frac{1}{1.2}=\frac{1}{9}-\frac{1}{10}-\frac{1}{8}+\frac{1}{9}-\frac{1}{7}+\frac{1}{8}-...-\frac{1}{2}+\frac{1}{3}-\frac{1}{1}+\frac{1}{2}\)

\(=\frac{2}{9}-\frac{1}{10}=\frac{20}{90}-\frac{9}{90}=\frac{11}{90}\)