9.4--The Direct Comparison Test (day #1)

When applying the Direct Comparison Test, you will usually compare a tricky series against a geometric series or a p-series whose convergence/divergence is already known.

Use the Direct Comparison Test to determine the convergence or divergence of the series: ∞ 1) 1 3 n + 7 n=1 9.4--The Direct Comparison Test (day #1)

Use the Direct Comparison Test to determine the convergence or divergence of the series: ∞ 2) 1

n - 2 n=3

Use the Direct Comparison Test to determine the convergence or divergence of the series: ∞ 3) 5n n 2 - 1 n=1 9.4--The Direct Comparison Test (day #1)

Use the Direct Comparison Test to determine the convergence or divergence of the series: ∞ 4) 1 n 4 + 3 n=1

9.4--The Limit Comparison Test (day #2)

The Limit Comparison Test is useful when the Direct Comparison Test fails, or when the series can't be easily compared with a geometric series or a p-series. 9.4--The Limit Comparison Test (day #2)

Use the Limit Comparison Test to determine the convergence or divergence of the series:

5) ∞ 3n2 - 2 n3 + 5 n=1

Use the Limit Comparison Test to determine the convergence or divergence of the series:

6) ∞ 4n5 + 9 10n7 n=1 9.4--The Limit Comparison Test (day #2)

Use the Limit Comparison Test to determine the convergence or divergence of the series:

7) ∞ 1 n 4 - 1 n=1

Use the Limit Comparison Test to determine the convergence or divergence of the series:

8) ∞ 5 3 2 n - 6 n=1 9.4--Comparisons of Series (day #3)

(This is actually a review of 9.1-9.4) page 630--Converging or diverging? Tell which test you used. ∞ 29) 3 n (C) p-Series Test n n=1

page 630--Converging or diverging? Tell which test you used. ∞ 30) n 7 (-1/7) (B) Geometric Series Test

n=0 9.4--Comparisons of Series (day #3)

(This is actually a review of 9.1-9.4) page 630--Converging or diverging? Tell which test you used. ∞ 31) 1 (F) Direct Comparison Test n 5 + 1 n=1

page 630--Converging or diverging? Tell which test you used. ∞ 32) 1 (F) Direct Comparison Test 3 n - 8 n=2 9.4--Comparisons of Series (day #3)

(This is actually a review of 9.1-9.4) page 630--Converging or diverging? Tell which test you used. ∞ 33) 2n (A) n-th Term Test 3n - 2 n=1

page 630--Converging or diverging? Tell which test you used. ∞ 34) 1 1 - (D) Telescoping Series Test n + 1 n + 2 n=1 9.4--Comparisons of Series (day #3)

(This is actually a review of 9.1-9.4) page 630--Converging or diverging? Tell which test you used. ∞ 35) n 2 2 (E) Integral Test (n + 1) n=1

page 630--Converging or diverging? Tell which test you used. ∞ 36) 3 (G) Limit Comparison Test n (n + 3) n=1 9.4--Comparisons of Series (day #3) page 631--Converging or diverging? How can you tell?

45)

∞ 1 200n n=1

46)

∞ 1 200+10n n=0

page 631--Converging or diverging? How can you tell?

47)

∞ 1 2 200 + n n=1

48)

∞ 1 3 200 + n n=1