Ta có: \(S=\frac{1}{2^2}-\frac{1}{2^4}+\frac{1}{2^6}-\frac{1}{2^8}+\cdots+\frac{1}{2^{2002}}-\frac{1}{2^{2004}}\)
=>4S=\(1-\frac{1}{2^2}+\frac{1}{2^4}-\frac{1}{2^6}+\cdots+\frac{1}{2^{2000}}-\frac{1}{2^{2002}}\)
=>4S+S=\(1-\frac{1}{2^2}+\frac{1}{2^4}-\frac{1}{2^6}+\cdots+\frac{1}{2^{2000}}-\frac{1}{2^{2002}}+1-\frac{1}{2^2}+\frac{1}{2^4}-\frac{1}{2^6}+\cdots+\frac{1}{2^{2000}}-\frac{1}{2^{2002}}\)
=>5S=\(1-\frac{1}{2^{2002}}\)
=>5S<1
=>S<0,2
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