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Math and science::Analysis::Tao::06. Limits of sequences

Square root, expressed as the limit of a sequence

Let \( c \in \mathbb{R} \) be a real. The sequence defined recursively below converges, and it converges to \( \sqrt{c} \).

Let \( x_1 = c \), and let \( x_n \) be defined like so:

[\[ x_{n + 1} = ?(x_n + \; ?) \]]