Đáp án :
a,
Đặt A = $\frac{3}{2}$ + $\frac{3}{8}$ + $\frac{3}{32}$ + $\frac{3}{128}$ + $\frac{3}{512}$
⇔ 4A = 6 + $\frac{3}{2}$ + $\frac{3}{8}$ + $\frac{3}{32}$ + $\frac{3}{128}$
⇔ 4A - A = ( 6 + $\frac{3}{2}$ + $\frac{3}{8}$ + $\frac{3}{32}$ + $\frac{3}{128}$ )
- ( $\frac{3}{2}$ + $\frac{3}{8}$ + $\frac{3}{32}$ + $\frac{3}{128}$ + $\frac{3}{512}$ )
⇔ 3A = 6 - $\frac{3}{512}$
⇔ A = $\frac{1 023}{512}$
⇒ $\frac{3}{2}$ + $\frac{3}{8}$ + $\frac{3}{32}$ + $\frac{3}{128}$ + $\frac{3}{512}$ = $\frac{1 023}{512}$
b,
Đặt B = 3 + $\frac{3}{5}$ + $\frac{3}{25}$ + $\frac{3}{125}$ + $\frac{3}{625}$
⇔ 5B = 15 + 3 + $\frac{3}{5}$ + $\frac{3}{25}$ + $\frac{3}{125}$
⇔ 5B - B = ( 15 + 3 + $\frac{3}{5}$ + $\frac{3}{25}$ + $\frac{3}{125}$ )
- ( 3 + $\frac{3}{5}$ + $\frac{3}{25}$ + $\frac{3}{125}$ + $\frac{3}{625}$ )
⇔ 4B = 15 - $\frac{3}{625}$
⇔ B = $\frac{2 343}{625}$
⇒ 3 + $\frac{3}{5}$ + $\frac{3}{25}$ + $\frac{3}{125}$ + $\frac{3}{625}$ = $\frac{2 343}{625}$
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