Examine the series
U=n=1∑∞n3+13n+2.
Answer each part below.
a. Identify a simpler positive–term series V whose convergence or divergence can be decisively established and that can be used to compare with U. State V explicitly and justify why it is an appropriate choice.
b. Using an appropriate comparison, determine whether U converges or diverges. Show all steps in your comparison and state any limits you evaluate.
c. Classify U as absolutely convergent, conditionally convergent, or divergent. Explain your reasoning clearly.