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2+2^2+2^3+...+2^n=2^55-2

Răspuns :

Matepentrutoti
[tex]2(1+2+2^2+...+2^{n-1})=2(2^{54}-1)\\ 1+2+..+2^{n-1}=2^{54}-1\\ 2^n-1=2^{54}-1\\ n=54.[/tex]
Mai2001
formula pt a+a²+a³+...+a^n= a^n*a- a( ultimul termen* ratia-primul termen)

2+2²+2³+...+2^n= 2^54*2-2=> 2^n= 2^54=> n= 54

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