Question

Chứng minh rằng:

 

Answer 1

Ta có: \(S=\frac{1}{2^2}-\frac{1}{2^4}+\frac{1}{2^6}-\cdots+\frac{1}{2^{4n-2}}-\frac{1}{2^{4n}}+\cdots+\frac{1}{2^{2002}}-\frac{1}{2^{2004}}\)

=>\(S=\frac{1}{2^2}-\frac{1}{2^4}+\cdots+\frac{1}{2^{2002}}-\frac{1}{2^{2004}}\)

=>4S=\(1-\frac{1}{2^2}+\ldots+\frac{1}{2^{2000}}-\frac{1}{2^{2002}}\)

=>4S+S=\(1-\frac{1}{2^2}+\ldots+\frac{1}{2^{2000}}-\frac{1}{2^{2002}}+\frac{1}{2^2}-\frac{1}{2^4}+\cdots+\frac{1}{2^{2002}}-\frac{1}{2^{2004}}\)

=>5S=\(1-\frac{1}{2^{2004}}\)

=>5S<1

=>S<0,2