Josephood7

Match each of the following with the correct statement.
C stands for Convergent, D stands for Divergent.
For each sequence anan find a number k such that nkannkan
has a finite non-zero limit.
(This is of use, because by the limit comparison test the series ∑n=1∞an∑n=1∞an and ∑n=1∞n−k∑n=1∞n−k both converge or both diverge.)

Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for "correct") if the argument is valid, or enter I (for "incorrect") if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.)
 The series ∑n=1∞nkrn∑n=1∞nkrn converges when 0<r<10<r<1 and diverges when r>1r>1. This is true regardless of the value of the constant kk. When r=1r=1 the series is a p-series. It converges if k<−1k<−1 and diverges otherwise. Each of the series below can be compared to a series of the form ∑n=1∞nkrn∑n=1∞nkrn. For each series determine the best value of r and decide whether the series converges.