# Determine whether the following series converges or diverges: sum_(k = 1)

Determine whether the following series converges or diverges:
$$\displaystyle{\sum_{{{k}={1}}}^{\infty}}\frac{{3}}{{\left({k}+{4}\right)}^{{3}}}$$

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Velsenw

$$\displaystyle{\sum_{{{k}={1}}}^{\infty}}\frac{{3}}{{\left({k}+{4}\right)}^{{3}}}=$$
$$\displaystyle={\sum_{{{k}={1}}}^{\infty}}\frac{{3}}{{k}^{{3}}}$$
By p-series test $$\displaystyle{\sum_{{{k}={1}}}^{\infty}}\frac{{1}}{{h}^{{p}}},{p}{>}{1}$$ – converges, $$\displaystyle{p}{<}{1}$$ – diverges.
So this series converges, cause it’s a p-series with p = 3.