Giải thích các bước giải:
a.Ta có :
$A_m=\dfrac{1}{1.99}+\dfrac{1}{3.97}..+\dfrac{1}{97.3}+\dfrac{1}{99.1}$
$\rightarrow 100A_m=\dfrac{100}{1.99}+\dfrac{100}{3.97}..+\dfrac{100}{97.3}+\dfrac{100}{99.1}$
$\rightarrow 100A_m=\dfrac{1+99}{1.99}+\dfrac{3+97}{3.97}..+\dfrac{97+3}{97.3}+\dfrac{99+1}{99.1}$
$\rightarrow 100A_m=\dfrac{1}{1}+\dfrac{1}{99}+\dfrac{1}{3}+\dfrac{1}{97}+..+\dfrac{1}{99}+\dfrac{1}{1}$
$\rightarrow 100A_m=2(1+\dfrac{1}{3}+\dfrac{1}{5}+..+\dfrac{1}{99})$
$\rightarrow A_m=\dfrac{1}{50}(1+\dfrac{1}{3}+\dfrac{1}{5}+..+\dfrac{1}{99})$
$\rightarrow A=\dfrac{1+\dfrac{1}{3}+\dfrac{1}{5}+..+\dfrac{1}{99}}{A_m}=50$