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Limit Comparison Test
Worksheet
Grade Level
Calculus II
CAL2.123 Limit Comparison Test
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Use the Limit Comparison Test for sum_{n=1}
infty
n(sqrt(n
2
+1)-n)
2
. Which benchmark and conclusion are valid?
A
Compare with sum 1/n; lim a_n/(1/n) = 1/4; since sum 1/n diverges (harmonic series), the given series diverges.
B
Compare with sum 1/n
2
; lim a_n/(1/n
2
) is positive and finite; since sum 1/n
2
converges (p = 2 > 1), the given series converges.
C
Compare with sum 1/n; lim a_n/(1/n) = 0, so the standard Limit Comparison Test gives no convergence conclusion.
D
Compare with sum 1/n; lim a_n/(1/n) = 1/4; the given series converges.
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