#!/usr/bin/python3

# https://math.stackexchange.com/a/943050/185635

from operator import mul
from functools import reduce
from math import isclose

def choose(n, k):
  if k + k > n: k = n - k
  numer = reduce(mul, range(n, n - k, -1), 1)
  denom = reduce(mul, range(1, k + 1), 1)
  return numer // denom

def sum1(n, m, p):
  f = lambda k: choose(k - 1, n - 1) * (1 - p)**k
  return (p / (1 - p))**n * sum(f(k) for k in range(n, n + m))

def sum2(n, m, p):
  f = lambda k: choose(n + m - 1, k) * (p / (1 - p))**k
  return (1 - p)**(n + m - 1) * sum(f(k) for k in range(n, n + m))

def same(n, m, p):
  return isclose(sum1(n, m, p), sum2(n, m, p))

assert(same(5, 8, 0.2))
assert(same(19, 12, 0.8))