Get the most by viewing this topic in your current grade. Pick your course now.

  1. Root Test Overview
  1. Useful Limit Question Used for Root test
    Show that lim\limn →\infty n1n=1n^{\frac{1}{n}}=1. This fact is useful when doing the root test for infinite series.
    1. Convergence & Divergence of Root test
      Use the Root test to determine if the series converges or diverges. If the root test does not determine the convergence or divergence of the series, then resort to another test.
      1. n=1(3)n2n \sum_{n=1}^{\infty}\frac{(-3)^n}{2n}
      2. n=0(n)2n+1π12n \sum_{n=0}^{\infty}\frac{(n)^{2n+1}}{\pi^{1-2n}}
      3. n=1[n22n35+2n3]3n \sum_{n=1}^{\infty}[\frac{n^2-2n^3}{5+2n^3} ]^{3n}
      4. n=1nn3n \sum_{n=1}^{\infty}\frac{n^n}{3^n}