Sa se calculeze suma:
$1 + \frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + \frac{1}{3^{4}}$
Rezolvare
$S = 1 + \frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + \frac{1}{3^{4}} = $
$\frac{3^{4} + 3^{3} + 3^{2} + 3 + 1}{3^{4}} = $
$\frac{81 + 27 + 9 + 3 + 1}{81} = \frac{121}{81}$
$S = \frac{121}{81}$
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