I'm looking for the precise value of
$$\sqrt{1+\sqrt{2+\sqrt{3+\sqrt{4+...}}}}.$$
It has thus far resisted my attempts to find its value, and I was wondering if anyone could share some insight.
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What is a numerical approximation? – user126154 Jun 15 '20 at 19:42
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A numerical approximation is 1.75793. – Teddy Mishura Jun 15 '20 at 19:44
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1There is no known closed form for this expression. However, a value does exist. See the duplicate. – Rushabh Mehta Jun 15 '20 at 19:49
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Thank you for the quick response! I appreciate it greatly. – Teddy Mishura Jun 15 '20 at 19:52
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The OEIS sequence A072449 has helpful information about the value. – Somos Jun 15 '20 at 19:52