# Classify whether this series convergessum_(k = 1)^oo ((-1)^k xx k)

Classify whether this series converges $\sum _{k=1}^{\mathrm{\infty }}\frac{{\left(-1\right)}^{k}×k}{6{k}^{4}+1}$

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Ayesha Gomez

$\sum _{k=1}^{\mathrm{\infty }}\frac{{\left(-1\right)}^{k}×k}{6{k}^{4}+1}$
${a}_{k}=\frac{k}{6{k}^{4}+1}$
${b}_{k}=\frac{k}{6{k}^{4}+1}$
1) ${b}_{k}\ge 0$
2) $\underset{k+0}{lim}\frac{k}{6{k}^{4}+1}=0$
Then, by alternative series test we can converge.
The term of series are alternative and limit of absolute value is 0, so series converge by alternative series test.