Question

Xn+1 = Xn+2^n, onde X1 = 1

Answer 1

n=1

X1+1 = X1 + 2^1

X2 = 1 + 2 = 3

n=2

X2+1 = X2 + 2^2

X3 = 3 + 4 = 7

n=3

X3+1 = X3 + 2^3

X4 = 7 + 8 = 15

Xn = 2^(n - 1) -1 + 2^(n-1) = 2^(n-1) . 2 - 1

Xn = 2^n - 1