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1+2+[tex] 2^{2} + [/tex]2³ + .... + [tex] 2^{40} [/tex]

Răspuns :

Este o progresie geometrica
b1=1
q=2
n=41
=> Sn= b1*(q^n - 1)/(q-1)
=> S41=1*(2^41 - 1)/1=@=2^41-1
S = 1+2+2^2+2^3+..............2^40
2S=2+2^2+2^3+2^4+..........2^41 le scadem
S-2S=1-2^41
S=2^41 - 1