Chứng minh rằng : \(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}<\frac{9}{20}\)
Chứng minh rằng: \(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+..........+\frac{1}{1985}< \frac{9}{20}\)
Đặt \(A=\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+...+\frac{1}{243}\)
\(A=\frac{1}{3}+\left(\frac{1}{5}+\frac{1}{7}+\frac{1}{9}\right)+\left(\frac{1}{11}+\frac{1}{13}+\frac{1}{15}+...+\frac{1}{27}\right)+\left(\frac{1}{29}+\frac{1}{31}+\frac{1}{33}+...+\frac{1}{81}\right)+\left(\frac{1}{83}+\frac{1}{85}+\frac{1}{87}+...+\frac{1}{243}\right)\)
\(\Rightarrow A>\frac{1}{3}+\frac{1}{9}.3+\frac{1}{27}.9+\frac{1}{81}.27+\frac{1}{243}.81\)
\(=\frac{1}{3}.5\)
\(=\frac{5}{3}\)
\(\Rightarrow A>\frac{5}{3}>\frac{5}{4}\)
\(\Rightarrow A>\frac{5}{4}\)
\(\Rightarrow\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{397}>\frac{5}{4}\)
\(\Rightarrow1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{397}>\frac{9}{4}\)
\(\Rightarrow\frac{1}{5}.\left(1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{397}\right)>\frac{9}{4}.\frac{1}{5}\)
\(\Rightarrow\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}>\frac{9}{20}\)
Chứng minh rằng \(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}< \frac{9}{20}\)
Chứng minh rằng:
\(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+..........+\frac{1}{1985}< \frac{9}{20}\)
Chứng minh rằng:\(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}< \frac{9}{20}\)
Giúp mik va ạ!
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
Chứng minh:\(A=\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}< \frac{9}{20}\)
Chứng minh: \(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}<\frac{9}{20}\)
sao anh đăng lắm câu hỏi vậy ?
Chứng minh rằng : \(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+....+\frac{1}{1985}< \frac{9}{20}\)
là ních phụ của Lê Tài Bảo Châu
Đợi anh cái lúc đó nhìn nhầm đề bài :))
Chứng minh: \(\frac{1}{5}\)+\(\frac{1}{15}\)+\(\frac{1}{25}\)+ .........+\(\frac{1}{1985}\)<\(\frac{9}{20}\)
CMR:\(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}< \frac{9}{20}\)