Newton’s iteration for √2 is . Starting from , what is ?

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Newton’s Method for √2

Goldman SachsJane Street

Newton’s iteration for √2 is $x_{n+1} = \tfrac12\left(x_n + \tfrac{2}{x_n}\right)$ . Starting from $x_0 = 2$ , what is $x_1$ ?

Approach

Plug $x_0 = 2$ into the iteration.

Answer

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