Table 1 Values of the components of \(x_{n}\) and \(\|x_{n+1}-x_{n}\|\)
n | \(x^{1}_{n}\) | \(x^{2}_{n}\) | \(x^{3}_{n}\) | \(\|x_{n+1}-x_{n}\|\) |
|---|---|---|---|---|
1 | 2.0000 | 3.0000 | 4.0000 | 4.5762 |
2 | 3.3463 × 10−1 | 4.4135 × 10−1 | 5.9093 × 10−1 | 6.8947 × 10−1 |
3 | 5.4164 × 10−2 | 6.4209 × 10−2 | 8.6473 × 10−2 | 1.0297 × 10−1 |
4 | 8.4481 × 10−3 | 9.1707 × 10−3 | 1.2416 × 10−2 | 1.5088 × 10−2 |
5 | 1.2664 × 10−3 | 1.2838 × 10−3 | 1.7454 × 10−3 | 2.1608 × 10−3 |
6 | 1.8212 × 10−4 | 1.7606 × 10−4 | 2.4004 × 10−4 | 3.0176 × 10−4 |
7 | 2.5079 × 10−5 | 2.3641 × 10−5 | 3.2281 × 10−5 | 4.1013 × 10−5 |
8 | 3.3006 × 10−6 | 3.1068 × 10−6 | 4.2426 × 10−6 | 5.4163 × 10−6 |
9 | 4.1426 × 10−7 | 3.9941 × 10−7 | 5.4467 × 10−7 | 6.9425 × 10−7 |
10 | 4.9466 × 10−8 | 5.0206 × 10−8 | 6.8263 × 10−8 | 8.6332 × 10−8 |
11 | 5.6050 × 10−9 | 6.1673 × 10−9 | 8.3472 × 10−9 | 1.0419 × 10−8 |
12 | 6.0092 × 10−10 | 7.3997 × 10−10 | 9.9524 × 10−10 | 1.2216 × 10−9 |