Daca S= 2¹+2²+2³+...+2⁴⁵, Calculati ( S + 2 ) ÷ 128⁶ repede dau coroana
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Răspuns:
Explicație pas cu pas:
S = 2^1 + 2^2 + 2^3 + ...+ 2^45
2S = 2^2 + 2^3 + 2^4 + ....+ 2^46
2S - S = 2^2 + 2^3 + 2^4 + ...+ 2^46 - 2^1 - 2^2 - 2^3 - ..._2^45
S = 2^46 - 2^1 = 2^46 - 2
S + 2 = 2^46 - 2 + 2 = 2^46
128 = 2^7
128^6 = (2^7)^6 = 2^42
_________
2^46 : 2^42 = 2^4 = 16