Question

[Lê Thị Phương Vy]

1 Tính nhanh 

A= [ 1/10 - 1 ]  NHÂN [ 1/11/- 1] NHân ........[1/100 -1]

Answer 1

[I don't need you]

\(A=\left(\frac{1}{10}-1\right).\left(\frac{1}{11}-1\right)....\left(\frac{1}{100}-1\right)\))

\(A=\frac{-9}{10}.\frac{-10}{11}...\frac{-99}{100}\) ( lẻ thừa số nguyên âm)

\(A=\frac{-9}{100}\)

Answer 2

[Arima Kousei]

\(A=\left(\frac{1}{10}-1\right)\left(\frac{1}{11}-1\right)...\left(\frac{1}{100}-1\right)\)

\(\Rightarrow A=-\frac{9}{10}.\frac{-10}{11}...\frac{-99}{100}\)

\(\Rightarrow-A=\frac{9}{10}.\frac{10}{11}...\frac{99}{100}\)

\(\Rightarrow-A=\frac{9.10.11...99}{10.11...99.100}\)

\(\Rightarrow-A=\frac{9}{100}\)

\(\Rightarrow A=-\frac{9}{100}\)