Examine the series _ n=1 ^ (-1)^ n 3n^ 2 +5 4n^ 3 -n
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Examine the series
n=1∑∞(−1)n4n3−n3n2+5.
Which of the following correctly describes its convergence?
(a) It diverges because its terms do not tend to 0 (the limit is 43).
(b) It converges conditionally but not absolutely.
(c) It converges absolutely by the Ratio Test since n→∞limanan+1=43<1.
(d) It converges absolutely because the series of absolute values is a p-series with p>1.