def sum_of_numbers(start_number, end_number):

    # n self explanatory
    n = abs(end_number - start_number) + 1

    # n / 2 represents the number of pairs,
    # end_number+start_number
represents the total for each pair.
return (end_number + start_number) * (n / 2)

def sum_of_odds(start_number, end_number):
    """ start_number < end_number, start_number and end_number are odd """
    # When adding odd numbers (1 + 3 + 5 + 7 + ....... + 2n-1)
    # you will get (1, 4, 9, 16,.......,n**2), the total can be represented as
    # n**2, in order to find the total of the first, lets say 100 numbers,
    # we use 100/2**2(half even and half odd) which is 2500, it works!

    # To make this a-bit more general, lets say we want to find the odd
    # numbers from 5 to 11, its like adding  the whole thing which is 6**2 and
    # the we subtract the first 2 odd numbers ( 6**2 - 1 - 3)

    start_number_position = (start_number + 1) / 2
    end_number_position = (end_number + 1) / 2

    return (end_number_position)**2 - (start_number_position - 1)**2

def sum_of_evens(start_number, end_number):
   """start_number < end_number, start_number and end_number are even"""

    # To find even numbers total between 2 numbers, (e.g : 12->20)
    # We add the odd numbers before each even number (11+13+15+17+19) then we
    # add 1 for each number (1*5)

    return sum_of_odds(start_number-1, end_number-1)
    + (end_number - start_number)/2 + 1