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Choosing Between Ratio and Root Tests
Worksheet
Grade Level
Calculus II
CAL2.129 Choosing Between Ratio and Root Tests
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For the series sum_{n=1}
∞
(n
2
+1)
n
/(3n)^(2n), which option gives the better first choice between the Ratio and Root Tests?
A
Root Test; take the n-th root because the term is built from an n-th power or n-dependent exponent.
B
Ratio Test; compare a_(n+1) to a_n because factorials, products, or consecutive factors simplify cleanly.
C
Neither as the first choice; Ratio and Root Tests are likely inconclusive or less direct here.
D
Either Ratio or Root Test; both reduce the form to the same simple exponential or geometric limit.
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