1. 12.3-12.4 Positive-Term Series, Integral Test, P-series,
Basic Comparison Test,
Limit Comparison Test.
Mathboat.com

2. Сover-Up Method:

3. SOLUTION:

4. SOLUTION:
p-series,
converges when 5k-3>1

5. SOLUTION:
p-series, p=3>1
convergent

6. SOLUTION: p-series, p=3>1 convergent p-series, p= <1 divergent
Harmonic series
divergent
p-series, p= <1
divergent

7. I. II. III. LCT Then both series either converges or diverges Diverges
To get , delete the terms of the least magnitude. I.
Diverges
Since Diverges, diverges also. So series DIVERGES.
P-Series, P>1, converges
II.
III.
Is geometric,
<1,
Converges

8. Solution: Theorem: = Then both series converge or both diverge.
Since Diverges, diverges also. So series DIVERGES.

9. >0 Then both series either converges or diverges
Delete terms of the
least magnitude
>0

11. Test each series separately.
series converges.
II.
Basic Comparison Test:

13. (A) I only. (C) I and III only. (E) I, II and III (B) II only
(A) I only (C) I and III only (E) I, II and III (B)  II only (D) II and III only NC

14. NC

15. None (C) I and III only (E) I, II and III
I and II only (D) II and III only