Convergence Tests Study Guide - Convergence of series The p-series 1 np is convergent if p > 1 and divergent if p 1 a rn1 is convergent if |r| < 1 and

Convergence Tests Study Guide - Convergence of series The...

This preview shows page 1 out of 1 page.

Convergence of seriesThe p-series.1npis convergent ifp >1 and divergent ifp1.The geometric series.a rn-1is convergent if|r|<1 and divergent if|r| ≥1.Test for Divergence.If limn→∞an6= 0 or the limit does not exist, thenanis divergent.The Integral Test.Supposefis a continuous, positive, decreasing function on [1,) and letan=f(n). Then the seriesanis convergent if and only if the improper integralR1f(x)dxisconvergent.The Comparison Test.Suppose that 0anbn.(a) Ifbnis convergent, thenanis also convergent.(b) Ifanis divergent, thenbnis also divergent.Limit Comparison Test.Letanandbnare positive numbers. If limn→∞anbn=cwith 0< c <, thenanis convergent if and only ifbnis convergent.

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture