Đề ??? :
\(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}>\frac{9}{20}\)
Giải
Đặt \(A=\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{243}\)
\(\Rightarrow A=\frac{1}{3}+\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)+\left(\frac{1}{11}+...+\frac{1}{27}\right)+\left(\frac{1}{29}+...+\frac{1}{81}\right)+\left(\frac{1}{83}+...+\frac{1}{243}\right)\)
\(\Rightarrow A>\frac{1}{3}+\frac{1}{9}.3+\frac{1}{27}.9+\frac{1}{81}.27+\frac{1}{243}.81\)
\(=\frac{1}{3}.5\)
\(=\frac{5}{3}\)
\(\Rightarrow A>\frac{5}{3}>\frac{5}{4}\)
\(\Rightarrow A>\frac{5}{4}\)
\(\Rightarrow\frac{1}{3}+\frac{1}{5}+...+\frac{1}{397}>\frac{9}{4}\)
\(\Rightarrow\frac{1}{5}.\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{397}\right)>\frac{9}{4}.\frac{1}{5}\)
\(\Rightarrow\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}>\frac{9}{20}\left(đpcm\right)\)
forever alone rai đề rùi
