MATH 1132Q Lecture Notes - Lecture 11: Direct Comparison Test, Ibm System P, Improper Integral

• School: UConn
• Department: Mathematics
• Course: MATH 1132Q
• Professor: Dr. David McArdle

Document Summary

In chapter 11. 3 we compared a series to a known improper integral to determine if the series converged or diverged. Now we will compare a given series to another series! If the terms of a given series are greater than (or equal to) the terms of a series that is known to be divergent, then the given series must. If the terms of a given series are less than (or equal to) the terms of a series that is known to be convergent, then the given series must. If is divergent and for all n, then is also divergent. If is convergent and for all n, then is also convergent. To determine if converges or diverges by comparison test: Determine a comparison series: look only at the higher power (or most dominant term) in the numerator and denominator to determine your comparison series. Use known results about geometric series and p-series. If comparison series diverges then you must show .