import sys
# Ask Python for a large stack. 
sys.setrecursionlimit(100000)

def pi_series_iter(n) :
    # Approximate (pi**2)/6 using n terms.  Based on the formula:
    # (pi**2)/6 = 1 + 1/4 + 1/9 + 1/16 + 1/25 + ...
    result = 0
    for i in range(1, n+1) :
        result = result + 1/(i**2)
    return result

def pi_approx_iter(n) :
    x = pi_series_iter(n)
    return (6*x)**(.5)

def pi_series_rec(n) :
    # As above, using recursion
    # Approximate (pi**2)/6 using n terms.  Based on the formula:
    # (pi**2)/6 = 1 + 1/4 + 1/9 + 1/16 + 1/25 + ...
    # Base case
    if n == 0 :
        return 0
    else :
        smaller_solution = pi_series_rec(n-1)
        solution = 1/n**2 + smaller_solution
        return solution

def pi_approx_rec(n) :
    x = pi_series_rec(n)
    return (6*x)**(.5)