F = \(\frac{1}{2}\) . \(\frac{2}{3}\) ..... \(\frac{98}{99}\) .\(\frac{99}{100}\)
\(\Leftrightarrow\)F = \(\frac{1.2.3...98.99}{2.3.4...99.100}\)
\(\Leftrightarrow\)F = \(\frac{1}{100}\)
Vậy F =\(\frac{1}{100}\)
\(F=\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)...\left(\frac{1}{100}-1\right)\)
\(F=\left(-\frac{1}{2}\right)\left(-\frac{2}{3}\right)...\left(-\frac{99}{100}\right)\)
F có : ( 99 - 1 ) : 1 + 1 = 99 phân số
=> F mang dấu âm
=> \(F=-\left(\frac{1}{2}\cdot\frac{2}{3}\cdot...\cdot\frac{99}{100}\right)\)
=> \(F=-\left(\frac{1\cdot2\cdot...\cdot99}{2\cdot3\cdot...\cdot100}\right)\)
=> \(F=-\frac{1}{100}\)