2. Sequences converging to P

From the plastic equation you have

fig101

that is

fig102

With a pocket calculator you get the following approximate values

1.0
1.259921049894873
1.3122938366832888
1.3223538191388249
1.324268744551578
1.3246326252509202
1.3247017485103587
1.3247148784409506
1.324717372435671
1.3247178461621454
1.324717936144965

It is possible to obtain more interesting sequences of rational terms.