Use the ratio test to determine whether ∑n=14∞n+2n! converges or diverges. (a) find the ratio of successive terms. write your answer as a fully simplified fraction. for n≥14, limn→∞∣∣∣an+1an∣∣∣=limn→∞.

The sum    diverges ∵ of the Ratio Test.

General Formulas and Concepts:
Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                       Special Limit Rule [Coefficient Power Method]:                                      

Series Convergence Tests

Ratio Test:                                                                                                        

Step-by-step explanation:

Step 1: Define

Identify.

Step 2: Find Convergence

[Series] Define:                                                                                             [Series] Set up [Ratio Test]:                                                                         [Ratio Test] Evaluate Limit [Coefficient Power Method]:                            [Ratio Test] Define conclusiveness:                                                          

Since infinity is greater than 1, the Ratio Test defines the sum    to be divergent.

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Learn more about the Ratio Test: link

Learn more about Taylor Series: link

Topic: AP Calculus BC (Calculus I + II)

Unit: Taylor Series

The answers are 20,30,80,180,960,890,1230,4560. on the first row