Giải thích các bước giải:
$M=1+\dfrac{1}{2}+\dfrac{1}{2^2}+..+\dfrac{1}{2^{100}}+\dfrac{1}{2^{100}}$
$\rightarrow 2M=2+1+\dfrac{1}{2}+..+\dfrac{1}{2^{99}}+\dfrac{1}{2^{99}}$
$\rightarrow 2M-M=2+\dfrac{1}{2^{99}}-\dfrac{1}{2^{100}}-\dfrac{1}{2^{100}}$
$\rightarrow M=2+\dfrac{1}{2^{99}}-2.\dfrac{1}{2^{100}}$
$\rightarrow M=2+\dfrac{1}{2^{99}}-\dfrac{1}{2^{99}}$
$\rightarrow M=2$