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Mình thấy là số cuối phai là 1/210 thì mới có quy luật chứ
Ta có:
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+...+\frac{1}{200}\)
\(A=\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+...+\frac{1}{14\times15}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{14}-\frac{1}{15}\)
\(A=\frac{1}{5}-\frac{1}{15}=\frac{2}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A= 1/30 +1/42+1/56+1/72+....+1/210
A=1/5x6 +1/6x7+1/7x8+1/8x9+...+1/14x15
A=1/5 -1/6+1/6-1/7+1/7-1/8+1/8-1/9+.....+1/14-1/15
A= 1/5 - 1/15
A= 2/15
\(\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{210}\)
=\(\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{14.15}\)
\(=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{14}-\frac{1}{15}\)=\(\frac{1}{5}-\frac{1}{15}\)
=\(\frac{3}{15}-\frac{1}{15}\)
=\(\frac{2}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{210}\)
\(A=\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+...+\frac{1}{14\cdot15}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+...+\frac{1}{14}-\frac{1}{15}\)
\(A=\frac{1}{5}-\frac{1}{15}=\frac{2}{15}\)
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{210}\)
\(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{14.15}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{14}-\frac{1}{15}\)
\(A=\frac{1}{5}-\frac{1}{15}\)
\(A=\frac{2}{15}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Gọi biểu thức đó là A
\(A=\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{110}\)
\(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}+\frac{1}{10.11}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)
\(A=\frac{1}{5}-\frac{1}{11}=\frac{11-5}{55}=\frac{6}{55}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110
= ( 1/5 - 1/6 ) + ( 1/6 - 1/7 ) + ... + ( 1/10 - 1/11 )
= 1/5 - 1/11 = 6/55
( Mình ko chắc chắn là đúng đâu nhé )
![](https://rs.olm.vn/images/avt/0.png?1311)
T = 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 + 1/110 + 1/132
T = 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 + 1/10.11 + 1/11.12
T = 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + 1/7 - 1/8 + 1/8 - 1/9 + 1/9 - 1/10 + 1/10 - 1/11 + 1/11 - 1/12
T = 1/4 - 1/12 (Cứ hai thằng cạnh nhau cộng lại bằng 0, chỉ còn thằng đầu và thằng cuối)
T = (3 - 1)/12
T = 2/12
T = 1/6
![](https://rs.olm.vn/images/avt/0.png?1311)
= 1/ 5.6 + 1/ 6.7 + 1/7.8 + 1/8.9 +.....+ 1/ 14.15
= 1/ 5 - 1/6 + 1/6 - 1/7 +......+1/14 - 1/15
= 1/5 - 1/ 15
= 3/15 - 1/15 = 2/ 15
![](https://rs.olm.vn/images/avt/0.png?1311)
8/9 - 1/72 - 1/56 - 1/42 - 1/30 - 1/20 - 1/12 - 1/6 - 1/2 = 0
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\\ =\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}\\ =\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\\ =\dfrac{1}{3}-\dfrac{1}{9}\\ =\dfrac{2}{9}\)
sai đề ở 1/200
uk 200 fai là 210 ms đúng