S=(1/1.3+1/3.5+.....+1/7.9)+(1/2.4+1/4.8+1/8.10)

2S=1/2.(1-1/3+1/5-1/5+....+1/7-1/9)+(1/2-1/4+1/4-1/8+1/8-1/10)

2S=1/2.(1-1/9)+(1/2-1/10)

2S=1/2.(8/9+2/5)

Đề như thế nào ý

2s=2/

4.9 hay 4.6

Ta có: \(2S=\dfrac{2}{1\cdot3}+\dfrac{2}{2\cdot4}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{7\cdot9}+\dfrac{2}{8\cdot10}\)

\(\Leftrightarrow2S=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{8}-\dfrac{1}{10}\)

\(\Leftrightarrow2S=1+\dfrac{1}{2}-\dfrac{1}{9}-\dfrac{1}{10}=\dfrac{58}{45}\)

\(\Rightarrow S=\dfrac{29}{45}\)

Ta có:

\(S=\dfrac{1}{1.3}+\dfrac{1}{2.4}+\dfrac{1}{3.5}+...+\dfrac{1}{7.9}+\dfrac{1}{8.10}\)

\(=\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{7.9}\right)\) \(+\left(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{8.10}\right)\)

Đặt \(A=\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{7.9}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{7.9}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{7}-\dfrac{1}{9}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{9}\right)=\dfrac{4}{9}\)

Đặt \(B=\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{8.10}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{8.10}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{8}-\dfrac{1}{10}\right)\)

\(=\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{10}\right)=\dfrac{1}{5}\)

\(\Rightarrow S=A+B=\dfrac{4}{9}+\dfrac{1}{5}=\dfrac{29}{45}\)

Vậy \(S=\dfrac{29}{45}\)

S=(1/1.3+1/3.5+.....+1/7.9) + (1/2.4+1/4.6+....+1/8.10)

2S=1/2.(1-1/9+(1/2-1/10))

2S=1/2.(8/9 + 2/5)

2S=1/2.58/45

2S=29/45

S=29/45:2

S=29/90

S=(1/1.3+1/3.5+.....+1/7.9) + (1/2.4+1/4.6+....+1/8.10)

2S=1/2.(1-1/9+(1/2-1/10))

2S=1/2.(8/9 + 2/5)

2S=1/2.58/45

2S=29/45

S=29/45:2

S=29/90

S = (1/1.3 + 1/3.5 + ... + 1/7.9) + (1/2.4 + 1/4.6 + ... + 1/8.10)

S = 2(1/1 - 1/3 + 1/3 - 1/5 + ... + 1/7 - 1/9) + 1/2(1/2 - 1/4 + 1/4 - 1/6 + ... + 1/8 - 1/10) 

S = 2.(1 - 1/9) + 1/2.(1/2 - 1/10)

S = 16/9 + 1/5 = 89/45

S= 1/1.3+ 1/2.4+1/3.5+....+!/7.9+1/8.10
=1/2(1-1/3 +1/2-1/4 +1/3-1/5 +...+ 1/7-1/9 + 1/8-1/10)
=1/2(1+1/2-1/9-1/10)
=....

\(S=\frac{1}{1.3}+.....+\frac{1}{8.10}\)

\(2S=\frac{2}{1.3}+....+\frac{2}{8.10}\)

\(2S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{8}-\frac{1}{10}\)

\(2S=1-\frac{1}{10}\)

\(2S=\frac{9}{10}\)

\(S=\frac{9}{10}:2\)

\(S=\frac{9}{20}\)

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