Ramanujan Second Problem

About a year ago, I wrote about one of my heroes, Ramanujan, and his first really cool problem: https://anothercasualcoder.blogspot.com/2018/02/ramanujan-first-problem.html. It turns out that he also had a less famous problem which went also unsolved for many, many years:

Sorry for the handwriting paint... In any case, this is an infinite series for which I have no idea how to solve, but with the help of some simple recursive code, you can pretty much find the solution in 5min. The code will be very similar to the first post, with the exception that I'm now passing two values (the "6" as v1, and the "2" as v2) as parameters, and the number of terms I want to process. In way than less than 70 terms, the function converges fast. The answer? 4 (four). Code and output are down below, cheers, ACC.

Code:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Ramanujan2
{
 class Program
 {
  static void Main(string[] args)
  {
   int max = 70;
   for (int i = 0; i <= max; i++)
   {
    Console.WriteLine("For terms = {0}, RSP = {1}", i, RamanujanSecondProblem(6, 2, 0, i));
   }
  }
  static double RamanujanSecondProblem(int v1, int v2, int terms, int maxTerms)
  {
   if (terms >= maxTerms) return 0.0;
   return Math.Sqrt(v1 + v2 * RamanujanSecondProblem(v1 + 1, v2 + 1, terms + 1, maxTerms));
  }
 }
}

Output:

For terms = 0, RSP = 0
For terms = 1, RSP = 2.44948974278318
For terms = 2, RSP = 3.36028311636522
For terms = 3, RSP = 3.72428093078256
For terms = 4, RSP = 3.87774468792224
For terms = 5, RSP = 3.94474031740102
For terms = 6, RSP = 3.97467867768177
For terms = 7, RSP = 3.98827831877827
For terms = 8, RSP = 3.99453082330687
For terms = 9, RSP = 3.99743199901717
For terms = 10, RSP = 3.9987879611993
For terms = 11, RSP = 3.99942546059194
For terms = 12, RSP = 3.99972664621995
For terms = 13, RSP = 3.99986952935495
For terms = 14, RSP = 3.99993755361378
For terms = 15, RSP = 3.99997003836743
For terms = 16, RSP = 3.99998559315209
For terms = 17, RSP = 3.9999930590532
For terms = 18, RSP = 3.99999665010797
For terms = 19, RSP = 3.99999838067683
For terms = 20, RSP = 3.9999992160921
For terms = 21, RSP = 3.99999962001047
For terms = 22, RSP = 3.99999981558073
For terms = 23, RSP = 3.99999991039593
For terms = 24, RSP = 3.99999995641879
For terms = 25, RSP = 3.99999997878278
For terms = 26, RSP = 3.99999998966129
For terms = 27, RSP = 3.99999999495796
For terms = 28, RSP = 3.99999999753915
For terms = 29, RSP = 3.99999999879806
For terms = 30, RSP = 3.99999999941254
For terms = 31, RSP = 3.99999999971269
For terms = 32, RSP = 3.9999999998594
For terms = 33, RSP = 3.99999999993115
For terms = 34, RSP = 3.99999999996627
For terms = 35, RSP = 3.99999999998347
For terms = 36, RSP = 3.99999999999189
For terms = 37, RSP = 3.99999999999602
For terms = 38, RSP = 3.99999999999805
For terms = 39, RSP = 3.99999999999904
For terms = 40, RSP = 3.99999999999953
For terms = 41, RSP = 3.99999999999977
For terms = 42, RSP = 3.99999999999989
For terms = 43, RSP = 3.99999999999994
For terms = 44, RSP = 3.99999999999997
For terms = 45, RSP = 3.99999999999999
For terms = 46, RSP = 3.99999999999999
For terms = 47, RSP = 4
For terms = 48, RSP = 4
For terms = 49, RSP = 4
For terms = 50, RSP = 4
For terms = 51, RSP = 4
For terms = 52, RSP = 4
For terms = 53, RSP = 4
For terms = 54, RSP = 4
For terms = 55, RSP = 4
For terms = 56, RSP = 4
For terms = 57, RSP = 4
For terms = 58, RSP = 4
For terms = 59, RSP = 4
For terms = 60, RSP = 4
For terms = 61, RSP = 4
For terms = 62, RSP = 4
For terms = 63, RSP = 4
For terms = 64, RSP = 4
For terms = 65, RSP = 4
For terms = 66, RSP = 4
For terms = 67, RSP = 4
For terms = 68, RSP = 4
For terms = 69, RSP = 4
For terms = 70, RSP = 4