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The Root Test: Let k=1akbe a series with nonnegative terms, and letp=limk___

If ρ < 1, the series ___.

If ρ > 1, the series ___.

If ρ = 1, ___.

Short Answer

Expert verified

Let k=1akbe a series with nonnegative terms, and let localid="1649361486379" p=limkakk.

If p<1, the series diverges.

If p>1, the series converges.

If p=1, the test is inconclusive.

Step by step solution

01

Step 1. Given Information

The given test is the root test.

02

Step 2. Explanation

  • To perform the root test, findp=limkakk
  • If p<1, the series is convergent.
  • If p>1, the series is divergent.
  • But if the limit is 1, the test cannot guarantee any behavior.

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