Positive-Term Series, Integral Test, P-series,

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Presentation transcript:

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

Сover-Up Method:

SOLUTION:

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

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

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

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

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

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

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

(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

NC

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