Question

[๖ۣۜҨž乡яσяσиσα zσяσღ]

CMR: \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{63}>2\)

Answer 1

[Lê Thị Mỹ Hằng]

S\(=\)\(\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{62}\right)\)\(+\)\(\left(\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+....+\frac{1}{63}\right)\)

 ta thấy S1=\(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{62}\)có 31 số

\(\frac{1}{61}< \frac{1}{2},\frac{1}{62}< \frac{1}{4}...\)\(\Rightarrow\)S1 > \(\frac{1}{62}+\frac{1}{62}+..+\frac{1}{62}\)( có 31 số ) \(=\frac{31}{62}=\frac{1}{2}\)

S2 = \(\frac{1}{3}+\frac{1}{5}+...+\frac{1}{63}\)( có 31 số )

ta thấy \(\frac{1}{63}< \frac{1}{3},\frac{1}{63}< \frac{1}{5}...\)\(\Rightarrow\)S2 > \(\frac{1}{63}+\frac{1}{63}+...+\frac{1}{63}\)( có 31 số ) \(=\frac{31}{63}=\frac{1}{3}\)

S1 + S2 > \(\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\)

=> S > 2