Project Euler 197 - Investigating the behaviour of a recursively defined sequence

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Thought Process

After investigating on WolframAlpha I saw that (un + un+1) would quickly converge to around 1.7 so I just made a while loop and once I got 2 sums that where the same up till the 10th decimal place, I stopped the program, and it was the correct answer, only takes about 518 iterations, which is a but less than 10^12.

Interactive Code

No interactive code, my code is given below