Exercise: iterative error with e^0.5
Approximating by its Taylor series, adding terms until the percentage iterative error drops below 0.05 %.
Iterate to tolerance
We use the series and add terms, computing the percentage iterative error after each (four decimals throughout).
| k | Approximation of e^{0.5} | Iterative error ε_{k,r} |
|---|---|---|
| 0 | 1 | n/a |
| 1 | 1.5 | 33.33 % |
| 2 | 1.625 | 7.6923 % |
| 3 | 1.6458 | 1.2658 % |
| 4 | 1.6484 | 0.1577 % |
| 5 | 1.6487 | 0.0181 % |