Question 9 (4 points) \( \quad \) srved
From the series listed below, select ALL convergent series.
\[
\sum_{n=1}^{\infty} \frac{(-1)^{n}}{\sqrt{n+3}}
\]
\[
\sum_{n=1}^{\infty} \frac{(2 n+1) !}{3^{n}}
\]
\[
\sum_{n=1}^{\infty} \frac{\sqrt{n^{2}+1}}{n^{3}+5}
\]
\[
\sum_{n=1}^{\infty}(-1)^{n} \frac{n}{n+1}
\]
Apply the alternating series test to \( \sum_{n=1}^\infty (-1)^n \frac{n}{n+1} \).
Step 1 :Apply the alternating series test to \( \sum_{n=1}^\infty \frac{(-1)^n}{\sqrt{n+3}} \).
Step 2 :Determine the convergence of \( \sum_{n=1}^\infty \frac{(2n+1)!}{3^n} \) using the ratio test.
Step 3 :Examine the convergence of \( \sum_{n=1}^\infty \frac{\sqrt{n^2+1}}{n^3+5} \) by comparing with a known convergent series.
Step 4 :Apply the alternating series test to \( \sum_{n=1}^\infty (-1)^n \frac{n}{n+1} \).