Calculating Pi - Infinite Series
The Leibniz formula for π states that
...
Which can be represented as
...
| n | sum | sum * 4 |
|---|---|---|
| 0 | 1 | 4 |
| 1 | 0.6666666667... | 2.6666666667... |
| 2 | 0.8666666667... | 3.4666666667... |
| 3 | 0.7238095238... | 2.8952380952... |
| 4 | 0.8349206349... | 3.3396825397... |
| 5 | 0.7440115440... | 2.9760461760... |
| 6 | 0.8209346209... | 3.2837384837... |
| 7 | 0.7542679543... | 3.0170718171... |
| 8 | 0.8130914837... | 3.2523659347... |
| 9 | 0.7604599047... | 3.0418396189... |
| 10 | 0.8080789524... | 3.2323158094... |
| 11 | 0.7646006915... | 3.0584027659... |
| 12 | 0.8046006915... | 3.2184027659... |
| 13 | 0.7675636544... | 3.0702546178... |
| 14 | 0.8020464131... | 3.2081856523... |
| 15 | 0.7697883485... | 3.0791533942... |
| 16 | 0.8000913789... | 3.2003655154... |
| 17 | 0.7715199503... | 3.0860798011... |
| 18 | 0.7985469773... | 3.1941879092... |
| 19 | 0.7729059517... | 3.0916238067... |
| 20 | 0.7972961956... | 3.1891847823... |
| 21 | 0.7740403816... | 3.0961615265... |
| 22 | 0.7962626038... | 3.1850504154... |
| 23 | 0.7749860081... | 3.0999440324... |
| 24 | 0.7953941714... | 3.1815766854... |
| 25 | 0.7757863282... | 3.1031453129... |
| ... | ... | ... |
| ∞ | 0.7853981634... | 3.1415926536... |