You may know from math that $$ \sum_{n=1}^\infty \frac 1n=\infty. $$ Let's see what we get using floating point:
import numpy as np
n = int(0)
float_type = np.float32
my_sum = float_type(0)
while True:
n += 1
last_sum = my_sum
my_sum += float_type(1 / n)
if n % 200000 == 0:
print("1/n = %g, sum0 = %g"%(1.0/n, my_sum))