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(Solved): Consider the series \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{3 n+19} \). Determine if the series conv ...
Consider the series \( \sum_{n=1}^{\infty} \frac{(-1)^{n}}{3 n+19} \). Determine if the series converges or diverges by examining the partial sums given below. \[ \begin{array}{l} S_{1}=-0.0454545454545455 \\ S_{2}=-0.00545454545454545 \\ S_{3}=-0.0411688311688312 \\ S_{4}=-0.00891076665270214 \\ S_{5}=-0.0383225313585845 \\ S_{6}=-0.0112955043315575 \\ S_{7}=-0.0362955043315575 \\ S_{8}=-0.0130396903780691 \\ S_{9}=-0.0347788208128517 \\ S_{10}=-0.0143706575475456 \end{array} \] Select the correct answer below: The series converges The series diverges