Question

So sánh:1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9 với 1

Giải chi tiết cho mình với: thank

Answer 1

Ta có:\(\frac{1}{2}>\frac{1}{8};\frac{1}{3}>\frac{1}{8};...;\frac{1}{6}>\frac{1}{8};\frac{1}{7}+\frac{1}{8}+\frac{1}{9}>\frac{3}{8}\)

\(\Rightarrow\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{3}{8}\)

                                                                 \(=\frac{8}{8}=1\)

Vậy\(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{9}>1\)