Question

Chứng minh rằng : \(\frac{1}{5}+\frac{1}{15}+\frac{1}{25}+...+\frac{1}{1985}<\frac{9}{20}\)

Answer 1

 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

Answer 2

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Answer 3

sai đề rùi đáng lẽ > 9/20

Answer 4

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Answer 5

Đúng rồi

Answer 6

Đặt A=1/5+1/15+1/25+...+1/1985

      A=1/5(1+1/3+1/5+...+1/397)<1/5(1+1-2/3+1-4/5+...+1-396/397)

                  =>       A               < 1/5[(1+1+...+1)-(2/3+4/5+..+396/397)]

                 =>       A                <1/5[200-(396/397+396/397+...+396/397)]

                                               <1/5.596/1985<1/5.9/4=9/20

                 

Answer 7

Xin lỗi nha cách đó không ổn rồi

Answer 8

hoi nhâm