Infinite Series Tests Around

the Room!

13 Review Problems

𝑛=1

∞(−1)𝑛5

𝑛

A. Diverges by the

Alternating Series Test

(Go to E)

B. Converges by the

Alternating Series Test

(Go to M)

C. Diverges by the Nth

Term Test

(Go to B)

D. Converges by the

Geometric Series Test

(Go to J)

𝑛=1

∞3

𝑛 𝑛

A. Diverges by the

Geometric Series Test

(Go to I)

B. Converge by the

Geometric Series Test

(Go to B)

C. Diverges by the p-

Series Test

(Go to J)

D. Converges by the

p-Series Test

(Go to G)

𝑛=1

∞−1 𝑛3𝑛−2

2𝑛

A. Diverges by the

Ratio Test

(Go to I)

B. Converges by the

Ratio Test

(Go to B)

C. Diverges by the p-

Series Test

(Go to J)

D. Converges by the

p-Series Test

(Go to A)

𝑛=1

∞2𝑛

4𝑛2 − 1

A. Diverges by the

Ratio Test

(Go to K)

B. Converges by the

Limit Comparison Test

(Go to F)

C. Converges by the

Ratio Test

(Go to L)

D. Diverges by the

Limit Comparison Test

(Go to E)

𝑛=1

∞2𝑛

𝑛 + 1

A. Diverges by the p-

Series Test

(Go to H)

B. Diverges by the Nth

Term Test

(Go to K)

C. Diverges by the p-

Series Test

(Go to A)

D. Converges by the

Nth Term Test

(Go to B)

𝑛=1

∞𝑛 ∗ 7𝑛

𝑛!

A. Diverges by the

Ratio Test

(Go to M)

B. Diverges by the

Comparison Test

(Go to C)

C. Converges by the

Ratio Test

(Go to L)

D. Converges by the

Comparison Test

(Go to G)

𝑛=1

∞(−1)𝑛3𝑛−1

𝑛!

A. Diverges by the

Ratio Test

(Go to D)

B. Diverges by the

Comparison Test

(Go to F)

C. Converges by the

Ratio Test

(Go to B)

D. Converges by the

Comparison Test

(Go to A)

𝑛=1

∞5

𝑛

A. Converges by

Geometric Series Test

(Go to J)

B. Diverges by

Geometric Series Test

(Go to F)

C. Converges by the

Ratio Test

(Go to M)

D. Diverges by

Harmonic Series

(Go to H)

𝑛=1

∞10

3 𝑛3

A. Diverges by p-Series

Test

(Go to M)

B. Diverges by

Geometric Series Test

(Go to A)

C. Converges by p-

Series Test

(Go to F)

D. Converges by

Geometric Series Test

(Go to I)

𝑛=1

∞𝑛

2𝑛2 + 1

A. Converges by

Comparison Test

(Go to M)

B. Diverges by Integral

Test

(Go to J)

C. Diverges by Ratio

Test

(Go to F)

D. Converges by

Integral Test

(Go to I)

𝑛=1

∞−1 𝑛

𝑛 ln 𝑛

A. Diverges by

Alternating Series Test

(Go to A)

B. Diverges by Integral

Test

(Go to K)

C. Converges by

Alternating Series Test

(Go to C)

D. Converges by

Integral Test

(Go to D)

𝑛=1

∞−1 𝑛3𝑛

𝑛 2𝑛

A. Diverges by Integral

Test

(Go to B)

B. Diverges by Ratio

Test

(Go to D)

C. Converges by

Integral Test

(Go to K)

D. Converges by Ratio

Test

(Go to L)

𝑛=1

∞𝜋

4

𝑛

A. Diverges by

Geometric Series Test

(Go to J)

B. Converges by

Geometric Series Test

(Go to A)

C. Converges by p-

Series Test

(Go to C)

D. Diverges by p-Series

Test

(Go to G)