# Determine whether the following series converges: sum_(k = 1)^oo (2/(k + 5)^3

Determine whether the following series converges: $$\displaystyle{\sum_{{{k}={1}}}^{\infty}}{\left(\frac{{2}}{{\left({k}+{5}\right)}^{{3}}}\right)}$$.

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hesgidiauE
$$\displaystyle{\sum_{{{k}={1}}}^{\infty}}{\left(\frac{{2}}{{\left({k}+{5}\right)}^{{3}}}\right)}$$
$$\displaystyle\lim_{{{k}\to\infty}}{\left({a}_{{k}}\right)}=\lim_{{{\left({k}\to{5}\right)}^{{5}}}}{\left(\frac{{2}}{{\left({k}+{5}\right)}^{{3}}}\right)}=\frac{{9}}{\infty}={0}$$
The limit of the terms of the series is 0, so the series diverges by the divergent test.