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Alternating Series Test
Worksheet
Grade Level
Calculus II
CAL2.124 Alternating Series Test
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Which proof correctly establishes convergence of ∑_{n=1}^∞ (-1)
n
(n
2
+4n)/(n
3
+1) by the Alternating Series Test?
A
b_n = (n
2
+4n)/(n
3
+1) is positive, approaches 0, and is decreasing for all sufficiently large n.
B
The signs alternate, so no other condition is needed.
C
The numerator grows, so b_n cannot approach 0.
D
The ratio of consecutive terms approaches 1, so the series diverges.
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