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- #1

So the solution goes as

Let $z_n$ be the nth term in the sequence $1,2,2,3,3,3,\ldots$.

Note that:

$$

\underbrace{\sum_{n=1}^{\infty}\frac{1}{|z_n|^3}}_{\text{Why to the 3rd power?}} = \underbrace{\sum_{n=1}^{\infty}\frac{n}{n^3}}_{ \text {Why is this equality true?}}

$$