calculați 1+3+3²+3³+...+3⁸⁰


Răspuns :

[tex]S=1+3+3^2+3^3+...+3^{80}|*3\\3S=3+3^2+3^3+...+3^{81}\\3S-S=3^{81}-1\\2S=3^{81}-1\\S=\frac{3^{81}-1}{2}[/tex]