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Use the ratio test to determine whether∑n=12∞n2+55n converges or diverges. (a) Find the ratio of successive...

Use the ratio test to determine whether∑n=12∞n2+55n converges or diverges.

(a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n≥12, limn→∞∣∣∣an+1an∣∣∣=limn→∞

(b) Evaluate the limit in the previous part. Enter ∞ as infinity and −∞ as -infinity. If the limit does not exist, enter DNE.
limn→∞∣∣∣an+1an∣∣∣ =  

(c) By the ratio test, does the series converge, diverge, or is the test inconclusive?

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