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Lecture

11.5 Alternating Series Question #2 (Medium)

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Department
Mathematics
Course Code
MAT136H1
Professor
all

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11.5 Infinite Sequences & Series Alternating Series Question #2 (Medium): Converging Series Against Alternating Series Test Strategy For an alternating series given as ∑ , it can be written as a more obvious alternating series like ∑ ( ) Alternating series test states that the series converges if it meets two conditions: 1) for all 2) Instead of working with n+1 and n, take the first derivative of the series function and see if . Only when the first derivative is negative, it is a decreasing function for all . Sample Question Test the series against the alternating series test for convergence or divergence. ( ) ∑ ( ) Solution Given the alternating series, [ ( )] (
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