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Is there a “big” command for square brackets as large as `\left[ … \right]`?

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I have the following LaTeX code (using amsmath and amssymb):

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 \documentclass[12pt]{article}  \usepackage{amsmath,amssymb} \begin{document} \[ \sum_{n=1}^{+\infty} \frac{\left(1 + \sin \frac{1}{n^2}\right)^{n^2}}{n^x} \] Consider the general term: \[ a_n = \frac{\left(1 + \sin \frac{1}{n^2}\right)^{n^2}}{n^x}    = \frac{\left(1 + \dfrac{1}{\frac{1}{\sin \frac{1}{n^2}}}\right)^{n^2}}{n^x}    = \frac{\Biggl[\left(1 + \dfrac{1}{\frac{1}{ \sin \frac{1}{n^2}}}\right)^{n^2}}{n^x} \] \end{document}

In the last line I used \Biggl[ hoping to make the square bracket as tall as a \left[ ...\right] delimiter. But \Biggl[ does not match the height of \left[ in my expression: the bracket doesn’t scale quite as much, especially when the content inside is very tall (because of exponents, fractions, etc.).

My questions are:

Is there a “size command” (\big, \Big, \bigg, \Bigg, or something else) for square brackets that produces exactly the same height as \left[ ...\right] in all cases?

If not, what is the best practice to get “manual brackets” that are almost as tall as \left[ ...\right], but without using \left/\right (e.g., to avoid weird spacing or other layout issues)?

Are there advanced TeX tricks (or uses of font parameters) to “force” bracket sizes even larger than standard \Bigg?


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