| 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())) |