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Free-Response Justification
Worksheet
Grade Level
Calculus II
CAL2.157 Free-Response Justification
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Which justification earns full credit for proving that sum_{n=1}
infty
n
2
/(n
4
+3) converges?
A
The terms are positive and decreasing, so the series converges.
B
Limit comparison with 1/n
2
: [n
2
/(n
4
+3)]/(1/n
2
)=n
4
/(n
4
+3) approaches 1; since sum 1/n
2
converges, the given series converges.
C
Compare with 1/n; since 1/n diverges, the series diverges.
D
The denominator has n
4
, so it is a p-series with p=4.
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