Nth Term Test for Divergence of an Infinite Series - Page 2

Questions
  • Using the first 10 terms graph the sequence, and use the graph to discuss the convergence or divergence of the sequence an=cos(npi/2)?
  • Does the series #a_n=(1+n)^(1/n)# converge or diverge?
  • How do i find the convergence or divergence of this series? #sum# from 1 to infinity of #1/n^lnn#
  • Determine whether or not the sequence with the given nth term is monotonic, then discuss its boundedness (i) an=cosn/n ?
  • Does #a_n = (1+1/n)^n# converge?
  • Dose #sum ((n^2+3)/(2+n^2))^(n^3)# with #n = 0 -> # infinity converge ?
  • Does the series converge or diverge?
  • Prove using the #epsilon-delta# method that #lim_(n->oo)= (2n)/(n^2+1) = 0# ?
  • How is the infinite series from n=0 to infinity of 3(2^(n+1))/5^n=10?
  • Prove using the #epsilon-delta# method that #lim_(n->oo) (2n^2+1)/(7n^2+n+5) = 2/7# ?
  • How to use test for divergence? #sum_(n=2) ^oo ((4+n)/n)^n#