When answering the following, keep in mind series and series tests that we have discussed …

"nth term" divergence test

telescoping

geometric

integral test

p-series

direct comparison

limit comparison

Tasks

1. Determine whether the series \( \displaystyle\sum_{n=1}^{\infty} \dfrac{2}{n^2 + 2n}\) is convergent or divergent by expressing the partial sums, \(S_N\), as a telescoping sum. If it is convergent, find its sum.

2. Test the series \( \displaystyle\sum_{m=1}^{\infty} \dfrac{6^{m+1}}{4^{5m}} \) for convergence or divergence. If the series is geometric and convergent, find its sum.