Question

[phi]

Cho B= 1/2 + 1/3 + 1/4 + ... + 1/63. So sánh B với 6

Answer 1

[Đoàn Đức Hà]

\(B=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}\)

\(=\left(\frac{1}{2}+\frac{1}{3}\right)+\left(\frac{1}{4}+...+\frac{1}{7}\right)+\left(\frac{1}{8}+...+\frac{1}{15}\right)+\left(\frac{1}{16}+...+\frac{1}{31}\right)+\left(\frac{1}{32}+...+\frac{1}{63}\right)\)

\(< \left(\frac{1}{2}+\frac{1}{2}\right)+\left(\frac{1}{4}+...+\frac{1}{4}\right)+\left(\frac{1}{8}+...+\frac{1}{8}\right)+\left(\frac{1}{16}+...+\frac{1}{16}\right)+\left(\frac{1}{32}+...+\frac{1}{32}\right)\)

\(=\frac{2}{2}+\frac{4}{4}+\frac{8}{8}+\frac{16}{16}+\frac{32}{32}=5< 6\)

Suy ra \(B< 6\).