Here are the consecutive sums:
| `1` | `=1` |
`1-1/6` |
`= 0.83333333` |
`1 - 1/6 + 1/120` |
`= 0.8416667` |
`1 - 1/6 + 1/120-1/5040` |
`= 0.8414683` |
`1 - 1/6 + 1/120-1/5040+1/362880` |
`= 0.8414710` |
`1 - 1/6 + 1/120-1/5040+1/362880-1/39916800` |
`= 0.8414710` |
The last value is the correct value of `sin 1` to six decimal places.