Table 3 Numerical results of \(\{x_{n}\}\), \(\{y_{n}\}\), and \(\{w_{n}\}\) with initial \(x_{1} = 1.0\) based on (3.12)
n | \(x_{n}\) | \(y_{n}\) | \(w_{n}\) |
|---|---|---|---|
1 | 1.000000000000000 | 0.66666666666667 | 1.333333333333333 |
2 | 0.292893218813452 | 0.15857864376269 | 0.475735931288071 |
3 | 0.347936514272221 | 0.07569664973395 | 0.378483248669752 |
4 | 0.290404855661242 | 0.03178852092125 | 0.286096688291246 |
5 | 0.221842355801224 | 0.01278310169095 | 0.217312728746085 |
6 | 0.167276133945363 | 0.00513758154788 | 0.169540191079954 |
7 | 0.12855725127519 | 0.00210398755141 | 0.136759190841874 |
8 | 0.101961142045651 | 0.00088311728422 | 0.113922129664937 |
9 | 0.083609952177013 | 0.00037957322278 | 0.097550318255454 |
10 | 0.070649802113264 | 0.00016648761182 | 0.085408144862541 |
11 | 0.061199308074553 | 0.00007423543142 | 0.07609131720753 |
12 | 0.054067201574777 | 0.00003353686476 | 0.068717035886434 |
13 | 0.048505907532604 | 0.00001530928652 | 0.062722146871100 |
14 | 0.044042300609567 | 0.00000704735258 | 0.057738959695359 |
15 | 0.040371134215207 | 0.00000326643477 | 0.053520533658321 |
16 | 0.037290303448763 | 0.00000152265596 | 0.049895913052360 |
17 | 0.034661992662647 | 0.00000071323249 | 0.046743117653451 |
18 | 0.032389319001134 | 0.00000033548179 | 0.043972605019241 |
19 | 0.030402139089697 | 0.00000015837395 | 0.041516938205506 |
20 | 0.028648273174303 | 0.00000007500477 | 0.039324174089535 |