Ta có:
A = $\dfrac{1}{3^{2}}$ + $\dfrac{1}{3^{3}}$ + $\dfrac{1}{3^{4}}$ + ... + $\dfrac{1}{3^{200}}$
$\dfrac{1}{3}$ . A = $\dfrac{1}{3}$ . ($\dfrac{1}{3^{2}}$ + $\dfrac{1}{3^{3}}$ + $\dfrac{1}{3^{4}}$ + ... + $\dfrac{1}{3^{200}}$)
= $\dfrac{1}{3^{3}}$ + $\dfrac{1}{3^{4}}$ + $\dfrac{1}{3^{5}}$ + ... + $\dfrac{1}{3^{201}}$
A - $\dfrac{1}{3}$ . A = ($\dfrac{1}{3^{2}}$ + $\dfrac{1}{3^{3}}$ + $\dfrac{1}{3^{4}}$ + ... + $\dfrac{1}{3^{200}}$) - ($\dfrac{1}{3^{3}}$ + $\dfrac{1}{3^{4}}$ + $\dfrac{1}{3^{5}}$ + ... + $\dfrac{1}{3^{201}}$)
$\dfrac{2}{3}$ . A = $\dfrac{1}{3^{2}}$ - $\dfrac{1}{3^{201}}$
A = $\dfrac{2}{3^{2}}$ - $\dfrac{2}{3^{201}}$
Bài 2:
Ta có: A = $\frac{1}{3}$ + $\frac{1}{3^{1}}$ + $\frac{1}{3^{2}}$ + ... + $\frac{1}{3^{200}}$
$\frac{1}{3}$ . A = $\frac{1}{3}$ . ($\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$ + ... + $\frac{1}{3^{200}}$)
= $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$ + $\frac{1}{3^{4}}$ + ... + $\frac{1}{3^{201}}$
A - $\frac{1}{3}$ . A = ($\frac{1}{3}$ + $\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$ + ... + $\frac{1}{3^{200}}$) - ($\frac{1}{3^{2}}$ + $\frac{1}{3^{3}}$ + $\frac{1}{3^{4}}$ + ... + $\frac{1}{3^{201}}$)
$\frac{2}{3}$ . A = $\frac{1}{3}$ - $\frac{1}{3^{201}}$
A = $\frac{2}{3}$ - $\frac{2}{3^{201}}$
