# Calculus: Other Calculus Problems – #27839

Question: Determine whether each of the series below is divergent, absolutely convergent (hence convergent) or conditionally convergent. Indicate the test, result or results you use to support your conclusion a- $$\sum\limits_{k=1}^{\infty }{\frac{\sqrt{k}}{\sqrt{k}+3}}$$ b- $$\sum\limits_{k=1}^{\infty }{\frac{{{\left( -1 \right)}^{k}}}{\sqrt{k\left( k+1 \right)}}}$$

c- $$\sum\limits_{k=1}^{\infty }{\frac{3{{k}^{2}}-1}{{{k}^{4}}}}$$

d- $$\sum\limits_{k=1}^{\infty }{\frac{\arctan \left( k \right)}{{{k}^{2}}}}$$

e- $$\sum\limits_{k=1}^{\infty }{\frac{{{\left( -1 \right)}^{n+1}}{{3}^{2n-1}}}{{{n}^{2}}+1}}$$

f- $$\sum\limits_{k=1}^{\infty }{\frac{{{5}^{k}}+k}{k!+3}}$$