# Lab 5, Task 5 (alternate)
# CptS 111
# John B. Schneider
#
# Alternate implementation to calculate:
#
#   f(x, k_max) = 1 + x + x ** 2 + x ** 3 + ... + x ** k_max
#               = x * (x * (x * (x * (1) + 1) + 1) + 1) + 1
#                 (where this is repeated k_max times)
#

def f(x, k_max):
    sum = 1.0
    for i in range(k_max):
        sum = x * sum + 1.0
    return sum