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2S=2/1.3+2/3.5+....+2/99.101
2S=1-1/3+1/3-1/5+....+1/99-1/101
2S=1-1/101
2S+1/101=1-1/101+1/101=1
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\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)
\(S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(S=1-\frac{1}{101}=\frac{100}{101}\)
\(2S+\frac{1}{101}=\frac{100}{101}\)
\(S=2.\frac{100}{101}+\frac{1}{101}\)
\(\Rightarrow S=\frac{201}{101}\)
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\(S=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)
\(2S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\)
\(2S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)
\(2S=1-\frac{1}{101}\Rightarrow2S+\frac{1}{101}=1\)
\(2S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+.........+\frac{1}{99}-\frac{1}{101}=1-\frac{1}{101}\)
\(2S+\frac{1}{101}=1-\frac{1}{101}+\frac{1}{101}=1\)
\(2S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+.....+\frac{2}{99.101}=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{99}-\frac{1}{101}\)
\(2S=1-\frac{1}{101}=\frac{100}{101}\)
\(S=\frac{50}{101}\)
S= 1/1.3 + 1/3.5 + 1/5.7 +................+ 1/200.202
=>S=1/2.(2/1.3+2/3.5+2/5.7+...+2/200.202)
=>S=1/2.(3-1/1.3+5-3/3.5+...+202-200/200.202)
=>S=1/2.(1-1/3+1/3-1/5+...+1/200-1/202)
=>S=1/2.(1-1/202)
=>S=1/2.201/202
=>S=201/404
Vậy S=201/404
\(2.S=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{2017.2019}\)
\(=\frac{3-1}{1.3}+\frac{5-3}{3.5}+\frac{7-5}{5.7}+...+\frac{2019-2017}{2017.2019}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}\)
\(=1-\frac{1}{2019}=\frac{2018}{2019}\)
=> \(S=\frac{1009}{2019}\)
Tính: S= 1/1.3 + 1/3.5 +1/5.7 + 1009/2019 .....+ 1/2017.2019
Trả lời:
1009/2019