\sum^{n+1}_{i=1}3^{\frac{i}{n+1}} - \sum^{n}_{i=1}3^{\frac{i}{n}} = \frac{2\sqrt[n+1]{3}}{\sqrt[n+1]{3}-1} - \frac{2\sqrt[n]{3}}{\sqrt[n]{3}-1} = \frac{2(\sqrt[n]{3}-\sqrt[n+1]{3})}{(\sqrt[n+1]{3}-1)(\sqrt[n]{3}-1)}