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Tremoros99
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4+3×4+3×4^2+3×4^3+....+3×4^2010

va roooooog​

Răspuns :

Rayzen

[tex]S = 4+3\cdot 4+3\cdot 4^2+3\cdot 4^3+...+3\cdot 4^{2010} \\ 4S =\quad\quad4^2+3\cdot 4^2+3\cdot 4^3+...+3\cdot 4^{2010}+3\cdot 4^{2011}\\ \noindent\rule{8.6cm}{0.7pt}\\ 4S-S = (3\cdot 4^{2011}+4^2) - (3\cdot 4+4) \\ 3S = 3\cdot 4^{2011}+4^2-4^2 \\ 3S = 3\cdot 4^{2011}\\ \\\Rightarrow \boxed{S = 4^{2011}}[/tex]

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