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ta có :
1/2 < 2/3
2/3 <3/4
.........
9999/10000 < 10000/10001
suy ra : A2 < 1/2*2/3*3/4******9999/10000*10000/10001
suy ra : A2 < 1/10001 < 1/10000= (1/100)2
suy ra A2 < (1/100)2 . Từ đó: A < 1/100 = 0,01
bài toán ddc chứng minh!!!!!!!!!!! ****
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có :
1/2 < 2/3
2/3 <3/4
.........
9999/10000 < 10000/10001
suy ra : A2 < 1/2*2/3*3/4******9999/10000*10000/10001
suy ra : A2 < 1/10001 < 1/10000= (1/100)2
suy ra A2 < (1/100)2 . Từ đó: A < 1/100 = 0,01
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta cóC= \(\dfrac{1}{2}.\dfrac{3}{4}.\dfrac{5}{6}......\dfrac{9999}{10000}\)
Đặt A = \(\dfrac{2}{3}.\dfrac{4}{5}.\dfrac{6}{7}.....\dfrac{10000}{10001}\)
Khi đó AC = \(\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}.....\dfrac{9999}{10000}.\dfrac{10000}{10001}\)= \(\dfrac{1}{10001}\)
Do \(\dfrac{1}{2}< \dfrac{2}{3}\)
\(\dfrac{3}{4}< \dfrac{4}{5}\)
.............
\(\dfrac{9999}{10000}< \dfrac{10000}{10001}\)
=> C<A=>C2<CA hay C2< \(\dfrac{1}{10001}\) , mà \(\dfrac{1}{10001}\)<\(\dfrac{1}{10000}\)=> C2< \(\dfrac{1}{10000}\)
Khi đó C < \(\sqrt{\dfrac{1}{10000}}\)hay C< \(\dfrac{1}{100}\)( đpcm )