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Calculus II
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Direct Comparison Test
Worksheet
Grade Level
Calculus II
CAL2.122 Direct Comparison Test
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For \(\sum_{n=1}
\infty
\frac{n
3
+2
n
}{n
5
+3
n
}\), which comparison proves convergence?
A
Since \(a_n\le1/n\), comparison with \(\sum1/n\) proves convergence.
B
Since \(\frac{n
3
+2
n
}{n
5
+3
n
}\le \frac{n
3
}{n
5
}+\frac{2
n
}{3
n
}=\frac{1}{n
2
}+(2/3)
n
\), compare with the sum of two convergent series.
C
Since \(a_n\ge(2/3)
n
\), comparison with a geometric series proves convergence.
D
Since the numerator has \(2
n
\), compare with \(\sum2
n
\) to prove divergence.
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