# version 1 of the Leibniz sum for pi (Exercise 2.17)

# int -> number
def leibniz(terms):
    """Returns the sum of the first terms of Leibniz's series for pi."""
    acc = 0
    num = 4
    den = 1
    multiplier = 1

    for aterm in range(terms):
        nextterm = num/den * multiplier
        acc = acc + nextterm
        den = den + 2
        multiplier = multiplier * -1

    return acc