Răspuns: Ai demonstrația mai jos
Explicație pas cu pas:
Salutare !
[tex]\large \bf B= 3+3^2+3^3+...+3^{2015}[/tex]
[tex]\large \bf B= (3^{1}+3^{2}+3^{3})+(3^{4}+3^{5}+3^{6})+...+(3^{2013}+3^{2014}+3^{2015})[/tex]
[tex]\large \bf B=3^{1}\cdot (3^{0}+3^{1}+3^{2})+3^{4}\cdot(3^{0}+3^{1}+3^{2})+...+3^{2013}\cdot(3^{0}+3^{1}+3^{2})[/tex]
[tex]\large \bf B=3^{1}\cdot (1+3+9)+3^{4}\cdot(1+3+9)+...+3^{2013}\cdot(1+3+9)[/tex]
[tex]\large \bf B=3^{1}\cdot 13+3^{4}\cdot 13+...+3^{2013}\cdot 13[/tex]
[tex]\color{red}\large \boxed{\bf B=13 \cdot (3^{1}+3^{4}+...+3^{2013})\implies B~\vdots~13}[/tex]
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