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Cum se rezolva 2+2^2+2^3+...+2^2015

Răspuns :

Se foloseste formula:
[tex]2+2^2+2^3+...+2^n = 2(2^n-1) = 2^{n+1}-2[/tex]
Atunci 2+2^2+2^3+...+2^n=2^(2015+1)-2 = 2^2016-2
   
[tex]2+2^2+2^3+...+2^{2015} = \frac{2^{2016} -2 }{2-1} =2^{2016} -2 [/tex]