Ai demonstratia mai jos
Explicație pas cu pas:
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[tex] \bf A =1+3^{1}+{3}^{2}+{3}^{3}+{3}^{4} + ...... + {3}^{2003} [/tex]
[tex]\bf A =(1+3^{1})+{3}^{2}\cdot({3}^{2 - 2}+{3}^{3 - 2})+{3}^{4}\cdot({3}^{4 - 4}+{3}^{5 - 4})+ ...... + {3}^{2002}\cdot({3}^{2002 - 2002}+{3}^{2003 - 2002})[/tex]
[tex]\bf A =(1+3)+{3}^{2}\cdot({3}^{0}+{3}^{1})+{3}^{4}\cdot({3}^{0}+{3}^{1})+ ...... +{3}^{2002}\cdot({3}^{0}+{3}^{1})[/tex]
[tex]\bf A =4+{3}^{2}\cdot(1+3)+{3}^{4}\cdot(1+3)+ ...... +{3}^{2002}\cdot(1+3)[/tex]
[tex]\bf A =4+{3}^{2}\cdot 4+{3}^{4}\cdot 4+ ...... +{3}^{2002}\cdot 4[/tex]
[tex]\bf A =4 \cdot(1+{3}^{2}+{3}^{4}+ ...... +{3}^{2002}) \: \vdots \: 4[/tex]
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