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Tough as introduction to analysis for beginners (Dutch handbook - I'm Belgian). Again ($n$) means index $n$, $x_1 = \sqrt6$, $x_{n+1} = \sqrt{6+x_n}$ Question: $$|x_{n+1} - 3| \le 1/5 \cdot |x_n - 3|... 4answers 12k views ### \sqrt{c+\sqrt{c+\sqrt{c+\cdots}}}, or the limit of the sequence x_{n+1} = \sqrt{c+x_n} (Fitzpatrick Advanced Calculus 2e, Sec. 2.4 #12) For c \gt 0, consider the quadratic equation x^2 - x - c = 0, x > 0. Define the sequence \{x_n\} recursively by fixing |x_1| \lt c and ... 1answer 392 views ### Sylow 2-subgroup of GL(2,R) I was trying to work out the Sylow p-subgroups for general linear groups over arbitrary fields, and was running into some trouble with non-algebraically closed fields. The real numbers, R, were ... 1answer 2k views ### Nested Square Roots 5^0+\sqrt{5^1+\sqrt{5^2+\sqrt{5^4+\sqrt\dots}}} How would one go about computing the value of X, where X=5^0+ \sqrt{5^1+\sqrt{5^2+\sqrt{5^4+\sqrt{5^8+\sqrt{5^{16}+\sqrt{5^{32}+\dots}}}}}} I have tried the standard way of squaring then trying ... 4answers 2k views ### Nested Radicals: \sqrt{a+\sqrt{2a+\sqrt{3a+\ldots}}} Let a>0 . How we can find the limit of :$$\sqrt{a+\sqrt{2a+\sqrt{3a+\ldots}}}$$Thanks in advance for your help 2answers 116 views ### Convergent Sequence Terminology What is the following sequence classified as? I don't want to make anybody solve it, I just need to know where to begin looking to solve it.$$\alpha_1 = \sqrt{20}\alpha_{n+1} = \sqrt{20 + \...
$\sqrt{2+\sqrt{2+\sqrt{2+\dots}}}$ $\dots\sqrt{2+\sqrt{2+\sqrt{2}}}$ Why they are different?
In Limit of the nested radical $\sqrt{7+\sqrt{7+\sqrt{7+\cdots}}}$ Timothy Wagner gave a correct answer that was questioned for not having shown that the limit exists in the first place. My question ...