def sum_till_n(n):
    """
        Returns the sum of the first n natural numbers till n
        Arguments:
            n -- the number till which sum is to be returned
        >>> sum_till_n(1)
        1
        >>> sum_till_n(10)
        55
        >>> sum_till_n(99)
        4950
    """
    return (n * (n + 1)) /2


def sum_squares_till_n(n):
    """
        Returns the sum of squares of the first n natural numbers till n
        Arguments:
            n -- the number till which sum is to be returned
        >>> sum_squares_till_n(1)
        1
        >>> sum_squares_till_n(10)
        385
        >>> sum_squares_till_n(99)
        328350
    """
    return (n * (n + 1) * (2*n + 1)) /6

def sum_cubes_till_n(n):
    """
        Returns the sum of cubes of the first n natural numbers till n
        Arguments:
            n -- the number till which sum is to be returned
        >>> sum_cubes_till_n(1)
        1
        >>> sum_cubes_till_n(10)
        3025
        >>> sum_cubes_till_n(99)
        24502500
    """
    t = sum_till_n(n)
    return (t * t)

def sum_powers_till_n(n, p):
    """
        Returns the sum of passeed power of the first n natural numbers till n
        Arguments:
            n -- the number till which sum is to be returned
            p -- the power which needs to be summed for first n natural numbers
        >>> sum_powers_till_n(1, 10)
        1
        >>> sum_powers_till_n(10, 2)
        385
        >>> sum_powers_till_n(99, 3)
        24502500
    """
    count = 1
    t = 0

    while count <= n:
        t = t + power(count, p)
        count = count + 1

    return t

# Sum of first n terms of arithmetic progression
# with a:first term and d:common difference
def sum_of_arithmetic_progression(n, a, d):
	return (n * (2*a + (n-1)*d)) / 2

# Sum of first n terms of geometric progression
# with a:first term and r:common ratio
def sum_of_geometric_progression(n, a, r):
	return (a * (1 - pow(r, n))) / (1 - r)

def power(a, n):
    res = 1

    while n != 0:
        if (n % 2) == 1:
            res = res * a

        a = a * a
        n = n / 2

    return res

if __name__ == '__main__':
    import doctest
    doctest.testmod()