Question

A=1/11+1/12+1/13+1/14+...+1/59+1/60

B=7/6

So sánh A và B?

Answer 1

\(A=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{60}=\left(\frac{1}{11}+...+\frac{1}{20}\right)+\left(\frac{1}{21}+...+\frac{1}{30}\right)+\left(\frac{1}{31}+...+\frac{1}{40}\right)+\left(\frac{1}{41}+...+\frac{1}{50}\right)+\left(\frac{1}{51}+...+\frac{1}{60}\right)_{\left(1\right)}>\frac{1}{20}.10+\frac{1}{30}.10+\frac{1}{40}.10+\frac{1}{50}.10+\frac{1}{60}.10=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}=\frac{29}{20}=\frac{87}{60}>\frac{70}{60}=\frac{7}{6}=B\)

(1): mỗi nhóm có 10 số hạng

=>A>B