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Does $\sum_{n=1}^\infty (-1)^n\dfrac{\sqrt{n}}{n+3}$ converge?
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Does $\sum_{n=2}^\infty \dfrac{(-1)^n n}{\ln{(n)}}$ converge or diverge?
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Does $\sum_{n=1}^\infty \dfrac{\cos{\left(n\pi\right)}}{\ln{\left(n\right)}}$ converge?
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Test $\sum_{n=1}^\infty \dfrac{(-1)^{n-1}5^{n-1}}{5^{n+1}n^{5/6}}$ for convergence.
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Does the series $\sum_{n=1}^\infty \dfrac{\cos{\left(\frac{n}{e^{\pi/e^2}}\right)}}{n^2}$ converge or diverge?