IMPROPER INTEGRALS THE COMPARISON TESTS In the comparison
- Slides: 11
IMPROPER INTEGRALS
THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) convg Known Series geometric P-series Example: Determine whether the series converges or diverges.
THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) divg Known Series geometric P-series Example: Determine whether the series converges or diverges.
THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) convg THEOREM: (THE COMPARISON TEST) divg
THE INTEGRAL TEST AND ESTIMATES OF SUMS TERM-112
THE COMPARISON TESTS In the comparison tests the idea is to compare a given series with a series that is known to be convergent or divergent. THEOREM: (THE COMPARISON TEST) divg Example: Determine whether the series converges or diverges.
THE COMPARISON TESTS THEOREM: (THE LIMIT COMPARISON TEST) both series converge or both diverge. With positive terms Example: Determine whether the series converges or diverges.
THE COMPARISON TESTS THEOREM: (THE LIMIT COMPARISON TEST) both series converge or both diverge. With positive terms Example: Determine whether the series converges or diverges. and Converge, then and divg, then convg divg Example: Determine whether the series converges or diverges. REMARK: Notice that in testing many series we find a suitable comparison series by keeping only the highest powers in the numerator and denominator.
THE INTEGRAL TEST AND ESTIMATES OF SUMS TERM-112
THE INTEGRAL TEST AND ESTIMATES OF SUMS TERM-111
THE COMPARISON TESTS Remarks: convg