4.9 hay 4.6

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)

S =\(\frac{1}{2}\left(1-\frac{1}{3}\right)+\frac{1}{2}\left(\frac{1}{2}-\frac{1}{4}\right)+....\frac{1}{2}\left(\frac{1}{8}-\frac{1}{10}\right)\)

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

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

S= 29/45

Bạn nói cô giáo sửa đề thành: 

Tính tổng S=1/1.3+1/2.4+1/3.5+.....+1/\(7\).9+1/8.10 

chứ không tổng S lẻ lắm, chẳng ai muốn tính cả.

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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