Dãy trên có 99 số
Vậy tích trên chắc chắn là số âm
1/2-1=-1/2
1/3-1=-2/3
..........
1/100-1=99/100
Ta có (1/2-1)(1/3-1)...(1/100-1)=(-1/2)(-2/3)...(-99/100)=-1/100
\(A=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right).....\left(\frac{1}{100}-1\right)\)
\(A=\left(-\frac{1}{2}\right)\left(-\frac{2}{3}\right).....\left(-\frac{99}{100}\right)\)
\(A=-\left(\frac{1}{2}.\frac{2}{3}.....\frac{99}{100}\right)\)
\(A=-\frac{1}{100}\)
Ta có: \(A=\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right)....\left(\frac{1}{100}-1\right)\)
\(\Rightarrow A=\left(-\frac{1}{2}\right).\left(\frac{-2}{3}\right)...\left(\frac{-99}{100}\right)\)
\(\Rightarrow A=-\left(\frac{1}{2}.\frac{2}{3}......\frac{99}{100}\right)=-\left(\frac{1.2.3...99}{2.3...100}\right)=\frac{-1}{100}\)
Vậy \(a=\frac{-1}{100}\)
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