Question

how to determine the nature of series

Answer 1

Answer:

You should recognize the form

(1+xn)n as it is a widely known property (sometimes even definition) of e, as limn→∞(1+xn)n=ex

Thus, the terms of your summation tend to ±e8 as m approaches infinity. Since the terms in your series need to converge to 0 for the series to converge, this series is divergent.