Question

aflati numarul n a)2+2²+2³+...+2^n=2⁵⁵-2
Pls dau corană​

Answer 1

Răspuns:

Explicație pas cu pas:

S = 2 + 2^2 + 2^3 + ...+ 2^n

2S = 2^2 + 2^3 + 2^4 + ...+ 2^n+1

2S - S = 2^2 + 2^3 + 2^4 + ...+ 2^n+1 - 2 - 2^2 - 2^3 - ...- 2^n

S = 2^n+1 - 2

2^n+1 - 2 = 2^55 - 2

2^n+1 = 2^55

n + 1 = 55

n = 55 - 1 = 54