# -*- coding: utf-8 -*-
"""
Created on Sun Jun 15 11:29:00 2025

@author: franc
"""

import matplotlib.pyplot as plt

def c(n,x):
    if n==0:
        return 1
    else:
        return (x-n+1)/n*c(n-1,x)
        
def s(N,x):
    S=0
    for n in range(N+1):
        S+=c(n,x)
    return S
    
lx=[-3+9*k/100 for k in range(101)]
for N in range(16):
    ly=[s(N,x) for x in lx]
    plt.plot(lx,ly)