Đặt A=1/3 + 1/5 +1/7 +1/9+.....+1/243

      A=1/3 +(1/5+1/7+1/9)+(1/11+1/13+1/15+....+1/27)+(1/29+1/31+1/33+.......+1/81)+(1/83+1/85+1/87+...+1/243)

    => A>1/3+ 1/9 x3+1/27 x9+1/81x27+ 1/243x81=1/3x5=5/3

  => A>5/3>5/4

=>A>5/4

   => 1/3+1/5+1/7+.....+1/397 > 5/4

  =>1+1/3+1/5+1/7+.....+1/397 > 9/4

 =>1/5x (1+1/3+1/5+1/7+.....+1/397)> 9/4 x 1/5

    =>1/5+1/15+1/25+......+1/1985 > 9/20

??????????????????????????????????????????????????

sai đề rùi đáng lẽ > 9/20

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

sao anh đăng lắm câu hỏi vậy ?

Bài anh có gì em tham khảo nhé 

Là sao??? Lê Tài Bảo Châu

là ních phụ của Lê Tài Bảo Châu 

Đợi anh cái lúc đó nhìn nhầm đề bài :))