Question

cho M = \(\frac{1}{15}+\frac{1}{105}+\frac{1}{315}+....+\frac{1}{9177}\). so sánh M với \(\frac{1}{12}\)

Answer 1

\(M=\frac{1}{15}+\frac{1}{105}+\frac{1}{315}+...+\frac{1}{9177}\)

\(M=\frac{1}{1.3.5}+\frac{1}{3.5.7}+\frac{1}{5.7.9}+...+\frac{1}{19.21.23}\)

\(M=\frac{1}{4}\left(\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{19.21}-\frac{1}{21.23}\right)\)

\(M=\frac{1}{4}\left(\frac{1}{1.3}-\frac{1}{21.23}\right)< \frac{1}{4}.\frac{1}{1.3}=\frac{1}{12}\)

\(\Rightarrow M< \frac{1}{12}\)