Question 1031251
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<pre>
There is even more simple formula

{{{R[n+1]}}} = {{{R[n]/cos(pi/n)}}}.      (1)

The table below is obtained from Excel, formula (1).

n	{{{cos(pi/n)}}}	{{{R[n]}}}
1	-	-
2	-	-
3	0.500000	1.000000
4	0.707107	2.000000
5	0.809017	2.828427
6	0.866025	3.496128
7	0.900969	4.036981
8	0.923880	4.480711
9	0.939693	4.849887
10	0.951057	5.161142
11	0.959493	5.426745
12	0.965926	5.655847
13	0.970942	5.855364
14	0.974928	6.030602
15	0.978148	6.185690
16	0.980785	6.323882
17	0.982973	6.447774
18	0.984808	6.559462
19	0.986361	6.660652
20	0.987688	6.752751
21	0.988831	6.836924
22	0.989821	6.914150
23	0.990686	6.985249
24	0.991445	7.050922
25	0.992115	7.111764
26	0.992709	7.168288
27	0.993238	7.220937
28	0.993712	7.270095
29	0.994138	7.316097
30	0.994522	7.359237
31	0.994869	7.399774
32	0.995185	7.437936
33	0.995472	7.473925
34	0.995734	7.507921
35	0.995974	7.540086
36	0.996195	7.570563
37	0.996397	7.599481
38	0.996584	7.626957
39	0.996757	7.653096
40	0.996917	7.677994
</pre>

Some info about this sequence see in the page <A HREF=https://oeis.org/A051762>https://oeis.org/A051762</A>.