Question

So sánh A với 1/21 biết A= (1-1/2).(1-1/3).(1-1/4) . ......(1-1/19).(1-1/20)

Answer 1

Ta có :

\(\left(1-\frac{1}{2}\right).\left(1-\frac{1}{3}\right).\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{19}\right).\left(1-\frac{1}{20}\right)\)

\(=\)\(\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.....\frac{18}{19}.\frac{19}{20}\)

\(=\)\(\frac{1.2.3.....18.19}{2.3.4.....19.20}\)

\(=\)\(\frac{1}{20}\)

Vì \(\frac{1}{20}>\frac{1}{21}\)nên \(A>\frac{1}{21}\)

Vậy \(A>\frac{1}{21}\)