1. Sec 11.4: 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
Example:
Determine whether the series
converges or diverges.
geometric
P-series

2. Sec 11.4: 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
Example:
Determine whether the series
converges or diverges.
geometric
P-series

3. Sec 11.4: 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

4. Sec 11.4: 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.

5. Sec 11.4: THE COMPARISON TESTS
THEOREM: (THE LIMIT COMPARISON TEST)
either both series converge or both diverge.
With positive terms
Example:
Example:
Determine whether the series
converges or diverges.
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.

6. Sec 11.3: THE INTEGRAL TEST AND ESTIMATES OF SUMS
TERM-092

7. Sec 11.3: THE INTEGRAL TEST AND ESTIMATES OF SUMS
REMAINDER ESTIMATE FOR THE INTEGRAL TEST

8. Sec 11.4: THE COMPARISON TESTS