Question

cho M = 1/10 + 1/15 + 1/21 + 1/28 + ....+ 1/105 + 1 /120.Chung to 1/3 < M < 1/2

Answer 1

cho tiền rồi giải cho

Answer 2

\(M=\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+...+\frac{1}{105}+\frac{1}{120}\)

\(M=\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+...+\frac{2}{210}+\frac{2}{240}\)

\(M=\frac{2}{4.5}+\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+...+\frac{2}{14.15}+\frac{2}{15.16}\)

\(M=\frac{2}{4}-\frac{2}{5}+\frac{2}{5}-\frac{2}{6}+\frac{2}{6}-\frac{2}{7}+\frac{2}{7}-\frac{2}{8}+...+\frac{2}{15}-\frac{2}{16}\)

\(M=\frac{2}{4}-\frac{2}{16}=\frac{3}{8}\)

Vì \(\frac{3}{9}< \frac{3}{8}< \frac{4}{8}\)nên \(\frac{1}{3}< M< \frac{1}{2}\)

Vậy \(\frac{1}{3}< M< \frac{1}{2}\)

P/S : Đừng nói như lần trước nhé!