\(x-\frac{6}{1.3.5}-\frac{6}{3.5.7}-...-\frac{6}{99.101.103}=0\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
2K = \(\frac{4}{1.3.5}+\frac{4}{3.5.7}+...............+\frac{4}{99.101.103}=\)\(\frac{1}{1.3}-\frac{1}{3.5}+\)\(+\frac{1}{3.5}-\frac{1}{5.7}+..................+\frac{1}{99.101}-\frac{1}{101.103}=\)
\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+................+\frac{1}{101}-\frac{1}{103}=1-\frac{1}{103}=\frac{102}{103}\)
=> K= \(\frac{102}{103}:2=\frac{51}{103}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\begin{equation} x = a_0 + \cfrac{1}{740_1 + \cfrac{1}{897654_2 + \cfrac{1}{672_3 + \cfrac{1}{100_4} } } } \end{equation}\)
Tính tổng :\(\frac{6}{1.3.5}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/1.3.5 + 1/3.5.7 + 1/5.7.9 +.....+ 1/99.101.103
= 1/4. [4/1.3.5 + 4/3.5.7 + 4/ 5.7.9 +....+ 4/99.101.103]
=1/4. [1/1.3 - 1/3.5 + 1/3.5 - 1/5.7 +....+ 1/99.101 - 1/101.103]
= 1/4. [1/1.3 - 1/101.103]
=1/4. 10406/31209
= 5230/62418
\(A=\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+....+\frac{1}{99\cdot101\cdot103}\)
\(2A=\frac{1}{1\cdot3}-\frac{1}{3\cdot5}+\frac{1}{3\cdot5}-\frac{1}{5-7}+....+\frac{1}{99\cdot101}-\frac{1}{101\cdot103}\)
\(2A=\frac{1}{1\cdot3}-\frac{1}{101\cdot103}\)
Tính nốt
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2E=\frac{6}{1.3.5}+\frac{6}{3.5.7}+...+\frac{3}{13.15.17}\)
\(2E=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{13.15}-\frac{1}{15.17}\)
\(2E=\frac{1}{1.3}-\frac{1}{15.17}\)
\(2E=\frac{1}{15}-\frac{1}{255}\)
\(\Rightarrow2E=\frac{16}{255}\)
\(\Rightarrow E=\frac{8}{255}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{1997.1999}-\frac{1}{1999.2001}\)
\(=\frac{1}{1.3}-\frac{1}{1999.2001}\)
Bạn tính kết quả nhé
X=1
TK MINH NHA