Question

1+3+3 la puterea 2 +..... +3 la puterea 2018​

Answer 1

$S = 1+3+3^2+...+3^{2018}\\\Leftrightarrow\,3S = 3+3^2+3^3+...+3^{2019}\\\Leftrightarrow\, 3S = (-1+1)+3+3^2+...+3^{2018}+3^{2019}}\\\Leftrightarrow\,3S = (1+3+3^2+...+3^{2018})+3^{2019}-1\\ \Leftrightarrow\,3S = S+3^{2019}-1\\\Leftrightarrow\,2S = 3^{2019}-1\\\\\Rightarrow \,\boxed{S = \dfrac{3^{2019}-1}{2}}$