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# finds sum of an infinite series such as
# a + a*x + a*x^2 + a*x^3 + a*x^4 + ...
# where constant is a and delta is x

def infinite_sum(constant, delta):
    output = (1-delta)**-1
    output *= constant
    return output

def finite_sum(constant, delta, n):
    top = constant * (1- delta**n)
    bottom = 1 - delta
    output = top / bottom
    return output