Root under the root with summation or product

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I have a question about an equation that I would like to obtain through either a product or a summation.

I would like to get a root sequence under roots that I can continue depending on n times:

$$\sqrt{2\sqrt{3\sqrt{4}}}$$

I would like to achieve the same result, but with a summation or a product.

And for days now I have been making attempts without obtaining concrete results Thank you very much