Giải thích các bước giải:
Ta có:
$A=\dfrac{1}{3^2}-\dfrac{1}{3^4}+...+\dfrac{1}{3^{4n-2}}-\dfrac{1}{3^{4n}}+...+\dfrac{1}{3^{98}}-\dfrac{1}{3^{100}}$
$\to 3^2A=1-\dfrac{1}{3^2}+...+\dfrac{1}{3^{4n}}-\dfrac{1}{3^{4n-2}}+...+\dfrac{1}{3^{96}}-\dfrac{1}{3^{98}}$
$\to 3^2A+A=1-\dfrac{1}{3^{100}}$
$\to A(3^2+1)=1-\dfrac{1}{3^{100}}$
$\to 10A=1-\dfrac{1}{3^{100}}<1$
$\to A<0.1$
