Question

Cho a=(1-1/2)*(1-1/3)*(1-1/4)*...*(1-1/19)*(1-1/20). So sanh a voi 1/21

Answer 1

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

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

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

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

\(A=\frac{1}{20}\Leftrightarrow A>\frac{1}{21}\)

Answer 2

\(A=\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right).....\left(1-\frac{1}{20}\right)\)

\(A=\frac{1}{2}.\frac{2}{3}......\frac{19}{20}=\frac{1}{20}>\frac{1}{21}\)

\(\text{Vậy: A lớn hơn 1/21}\)