(1+z_1/n)^n
orange dots show high n values (successive powers of 2 up to 1024)

green dots show successive k values
(1+z_1/n)^k

(1+(z_1)/n)^n  large n

n=1024

z_1 = (0.0010690828573714356, 3.1410063293089165)
n = 16 (slider from 1 to 100, step 1)
L_1 = Sequence((1 + z_1 / n)^(k), k, 1, n)
z_2: L_1(Length[L_1])
L_2 = Sequence((1 + z_1 / 2^(k))^(2^(k)), k, 1, 9)
z_3: (1 + z_1 / 2^(10))^(2^(10))