Question

CMR :

S = \(\frac{1}{2^2}-\frac{1}{2^4}+\frac{1}{2^6}-...+\frac{1}{2^{4n-2}}-\frac{1}{2^{4n}}+...+\frac{1}{2^{2002}}-\frac{1}{2^{2004}}<0,2\)

P/S : chtt mình không tích , không pít chtt là cái gì hết á

Answer 1

S = \(...\)

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

=> \(S.4+S=\left(1-\frac{1}{2^2}+\frac{1}{2^4}-...-\frac{1}{2^{2002}}\right)+\left(\frac{1}{2^2}-\frac{1}{2^4}+\frac{1}{2^6}-...-\frac{1}{2^{2004}}\right)\)

=> \(5S=1-\frac{1}{2^{2004}}<1\)

=> \(S<1:5=0,2\left(đpcm\right)\)

Vậy S < 0,2.