∞ (1 point) Consider the series Σan where an = (-1)"+7 In ( 1 + 'ın(1 + º). n n=1 Is the series (eventually) alternating? ? Are the terms of the series (eventually) nonincreasing in magnitude? ? What is the limit of the terms of the series? lim an = n→∞ Based on your answers above, can the alternating series test be applied to the series? ? Using the alternating series test or other tests, does the series converge or diverge? ? A
(1 point) Consider the series ∞ Ž n=1 3n (n +9)! an where an = = (−1)ª - Is the series (eventually) alternating? ? - Are the terms of the series (eventually) nonincreasing in magnitude? ? Using the alternating series test or other tests, does the series converge or diverge? ?
∞ (1 point) Consider the series Σa, where an = n=1 Find the sum of the first four terms of the series. S4 = - 1 n6 (−1)n+5 (Remember that you can make Webwork do your calculations for you!) Using the alternating series error estimation theorem, find a bound for the magnitude of the error in the above estimation. The absolute value of the difference between $4 and the entire sum is at most: Using your above answers, the value of the entire sum is between $4 and what other number? The sum between $4 and:
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