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

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