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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)