Question

Am nevoie urgent! Dau coroana! ​

Answer 1

$\displaystyle S_n=\sum_{k=1}^n \frac{6^k-1}{5} =\frac{1}{5} \sum_{k=1}^n\Big(6^k-1\Big)=\frac{1}{5} \Bigg(\sum_{k=1}^n 6^k-\sum_{k=1}^n1\Bigg)\\\\ \sum_{k=1}^n6^k=6^1+6^2+6^3+...+6^n=\frac{6\Big(6^n-1\Big)}{6-1} =\frac{6^{n+1}-6}{5} \\\\ \sum_{k=1}^n1=n$

$\displaystyle S_n=\sum_{k=1}^n \frac{6^k-1}{5} =\frac{1}{5} \sum_{k=1}^n\Big(6^k-1\Big)=\frac{1}{5} \Bigg(\sum_{k=1}^n 6^k-\sum_{k=1}^n1\Bigg)=\\\\=\frac{1}{5}\Bigg(\frac{6^{n+1}-6}{5} -n\Bigg)=\frac{1}{5} \cdot \frac{6^{n+1}-6-5n}{5} =\frac{1}{25}\Big(6^{n+1}-5n-6 \Big)$