"""
Compute the partial sums of infinite series.

File = demo01.py
"""

def sum1(n):
   """sum1(n) = 1 + 1/2 + 1/3 + ... + 1/n"""
   sum = 0
   i = 1
   while i <= n:
      sum = sum + 1.0/i
      i = i + 1
   return sum

def sum2(n):
   """sum2(n) = 1 - 1/2 + 1/3 - 1/4 + 1/5 + ... + (-1)^n/n"""
   sum = 0
   i = 1
   while i <= n:
      if i % 2 == 1:
         sum = sum + 1.0/i
      if i % 2 == 0:
         sum = sum - 1.0/i
      i = i + 1
   return sum

g = lambda x: 1.0/(x*x);

def sum(f,n):
   """sum(f,n) = f(1) + f(2) + ... + f(n)"""
   i = 1
   S = 0
   while i <= n:
      S = S + f(i)
      i = i + 1
   return S