Question

Daca S= 2¹+2²+2³+...+2⁴⁵, Calculati ( S + 2 ) ÷ 128⁶ repede dau coroana​

Answer 1

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