3. CMR $S=\dfrac{1}{2^2}-\dfrac{1}{2^4}+\dfrac{1}{2^6}-....+\dfrac{1}{2^{2002}}-\dfrac{1}{2^{2004}} <0,2$
ta có:
$S=\dfrac{1}{2^2}-\dfrac{1}{2^4}+\dfrac{1}{2^6}-....+\dfrac{1}{2^{2002}}-\dfrac{1}{2^{2004}}$
$S=\dfrac{1}{4}-\dfrac{1}{4^2}+\dfrac{1}{4^3}-.....+\dfrac{1}{4^{1001}}-\dfrac{1}{4^{1002}}$
=>$4S=1-\dfrac{1}{4}+\dfrac{1}{4^2}-...+\dfrac{1}{4^{1000}}-\dfrac{1}{4^{1001}}$
=>$4S+S=1-\dfrac{1}{4^{1002}}$
=>$5S=1-\dfrac{1}{4^{1002}}$
=>$S=\dfrac{1-\dfrac{1}{4^{1002}}{5}$
mà $0.2=\dfrac{1}{5}$
mà $\dfrac{1-\dfrac{1}{4^{1002}}}{5}<\dfrac{1}{5}$
=>đpcm