import numpy as np

from numpy import exp

def s1(x):
    
    y = 1 / ( 1 - x )
    
    return y

def s1e(x):

    y = 1 / (1 - (-exp(-x)))

    return y

def s2(x):

   max = 100

   sum = 0

   i = 0

   while (i < max):

       sum += x**i

       i += 1

   return sum

def s2e(x):

   max = 5000

   sum = 0

   i = 0

   while (i < max):

       sum += (-exp(-x))**i

       i += 1

   return sum
    
print(s1(-0.25))
print(s2(-0.25))

print(s1e(0.25))
print(s2e(0.25))