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Comparison and Integral Tests

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1. Apply the Basic Comparison Test (BCT) and Limit Comparison Test (LCT). Find an appropriate Comparison series to determine convergence or divergence. See attached file for formulas.

2. Apply the Integral Test: First use a method to see if the terms are decreasing, then to determine convergence or divergence. See attached file for formulas.

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Solution Summary

This solution shows how to perform a comparison test and integral test in a step-wise logical manner.

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The idea behind the limit comparison test is that if you take a known convergent series and multiply each of its terms by some number, then that new series also converges. Same applies to divergent series.

To determine benchmark series: Take the highest power of n in the numerator and the denominator - ignoring any coefficients and all other terms - then simplify.

You can discover whether such a connection exists between two series by looking at the ratio of the nth terms of the two series as n approaches infinity.

7. Benchmark series: n3 / n5 = 1/n2
Now take limit comparison test:
take the limit of the ratio of the nth terms of ...

Solution provided by:
Tania Dey, PhD
Education
  • BSc (Hons),
  • MSc,
  • PhD,
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