2¹+2²+2³+...+2^n=2⁵⁵-2
Daca inmultim toata propozitia cu 2, avem:
2²+2³+2⁴+...+2^n+2^(n+1)=2⁵⁶-2²
Adaugam (si scadem) un 2:
2 -2+ 2²+2³+2⁴+...+2^n+2^(n+1)=2⁵⁶-2²
(2 +2²+2³+2⁴+...+2^n) + 2^(n+1) -2= 2⁵⁶-2²
2⁵⁵-2 + 2^(n+1) -2= 2⁵⁶-2²
2⁵⁵ + 2^(n+1) -4= 2⁵⁶-4
2⁵⁵ + 2^(n+1) = 2⁵⁶
2^(n+1) = 2⁵⁶-2⁵⁵
2^(n+1) = 2⁵⁵(2-1)
2^(n+1) = 2⁵⁵
2^(n+1) = 2⁵⁴⁺¹
n+1=54+1
n=54
