File size: 740 Bytes
848d4b7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | from mpmath import mp
mp.dps = 110
def compute():
k = 6
# b_n = 1/binomial(2n,n), with recurrence:
# b_1 = 1/2
# b_n = b_{n-1} * n / (2*(2n-1))
b = mp.mpf(1) / 2
terms = [b] # n=1 term: b_1 / 1^6
# Truncation target far below 1e-100; tail is < (4/3)*last_term since ratio < 1/4
tol = mp.power(10, -(mp.dps + 15))
n = 1
while True:
n += 1
b *= mp.mpf(n) / (2 * (2 * n - 1))
term = b / (mp.mpf(n) ** k)
terms.append(term)
if term < tol and (mp.mpf(4) / 3) * term < tol:
break
if n > 100000:
raise RuntimeError("Failed to converge fast enough")
return mp.fsum(terms)
if __name__ == "__main__":
print(str(compute())) |