Question

 hãy so sánh A và B biết :

A=1 +1/2+1/3+1/4+...+ 1/15 +1/16 và B=3

Answer 1

Ta có\(A=1+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)+\left(\frac{1}{5}+\frac{1}{6}+\frac{1}{7}+\frac{1}{8}\right)+\left(\frac{1}{9}+\frac{1}{10}+\frac{1}{11}+\frac{1}{12}\right)+\left(\frac{1}{13}+\frac{1}{14}+\frac{1}{15}+\frac{1}{16}\right)\)\(>1+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)+4\times\frac{1}{8}+4\times\frac{1}{12}+4\times\frac{1}{16}\)

\(=1+\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\)

\(=1+2\times\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\right)\)

\(>1+2\times\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{4}\right)=1+2=3=B\)

\(\Rightarrow A>B\)