Questions: Determine whether the following series converges. ∑(k=1 to ∞)(-1)^(k+1) (k^22+4k^11+9)/(k(k^22+9)) Let ak ≥ 0 represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The series converges because ak= □ B. The series diverges because ak= □ C. The series converges because ak= and for any index N, there are some values of k>N for which ak+1 ≥ ak and some values of k>N for which ak+1 ≤ ak. and for any index N, there are some values of k>N for which ak+1 ≥ ak and some values of k>N for which ak+1 ≤ ak. □ is nonincreasing in magnitude for k greater than some index N and lim (k → ∞) ak= □ D. The series diverges because ak= □ nonincreasing in magnitude for k greater than some index N and lim (k → ∞) ak=□. E. The series diverges because ak=□ is nondecreasing in magnitude for k greater than some index N. F. The series converges because ak=□ is nondecreasing in magnitude for k greater than some index N.

Transcript text: Determine whether the following series converges. \[ \sum_{k=1}^{\infty}(-1)^{k+1} \frac{k^{22}+4 k^{11}+9}{k\left(k^{22}+9\right)} \] Let $a_{k} \geq 0$ represent the magnitude of the terms of the given series. Select the correct choice below and fill in the answer box(es) to complete your choice. A. The series converges because $\mathrm{a}_{\mathrm{k}}=$ $\square$ B. The series diverges because $a_{k}=$ $\square$ C. The series converges because $a_{k}=$ and for any index $N$, there are some values of $k>N$ for which $a_{k+1} \geq a_{k}$ and some values of $k>N$ for which $a_{k+1} \leq a_{k}$. and for any index $N$, there are some values of $k>N$ for which $a_{k+1} \geq a_{k}$ and some values of $k>N$ for which $a_{k+1} \leq a_{k}$. $\square$ is nonincreasing in magnitude for $k$ greater than some index $N$ and $\lim _{k \rightarrow \infty} a_{k}=$ $\square$ D. The series diverges because $a_{k}=$ $\square$ nonincreasing in magnitude for $k$ greater than some index $N$ and $\lim _{k \rightarrow \infty} a_{k}=\square$. E. The series diverges because $\mathrm{a}_{\mathrm{k}}=\square$ is nondecreasing in magnitude for k greater than some index N . F. The series converges because $\mathrm{a}_{\mathrm{k}}=\square$ is nondecreasing in magnitude for k greater than some index N .