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The Comparison Test: Let k=1akandk=1bkbe two series with ___ terms such that 0___ak___bkfor every positive integer k. If the series k=1bk___ , then the series k=1ak___.

Short Answer

Expert verified

Let k=1akandk=1bkbe two series with positive terms such that 0akbkfor every positive integer k. If the series k=1akdiverges, then the series k=1bk diverges.

Step by step solution

01

Step 1. Given Information.

The given test is the comparison test.

02

Step 2. Explanation

  • A comparison test is used if there are 2 positive series such that 0akbk.
  • If such series are found, the if k=1akdiverges, k=1bkalso diverges.
  • And if k=1bkconverges, k=1akalso converges.

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