# Tell whether the series converges or diverges. sum_(k = 1)^oo 5/(k + 4)^4

Tell whether the series converges or diverges.
$$\displaystyle{\sum_{{{k}={1}}}^{\infty}}\frac{{5}}{{\left({k}+{4}\right)}^{{4}}}$$

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Lacey-May Snyder
$$\displaystyle{\sum_{{{k}={1}}}^{\infty}}\frac{{5}}{{\left({k}+{4}\right)}^{{4}}}$$
Put $$\displaystyle{k}+{4}\Rightarrow{n}$$
So, $$\displaystyle{\sum_{{{n}={5}}}^{\infty}}\frac{{5}}{{n}^{{4}}}$$
From p-series test:
For series $$\displaystyle{\sum_{{{n}={1}}}^{\infty}}\frac{{1}}{{n}^{{p}}}$$, if p> 1, series converges.
So, for series in equation 1
P = 4, so this series converges
The series is p-series with p = 4 and it converges.