MAT136H1 Lecture Notes - Alternating Series Test, Alternating Series
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MAT136H1 Full Course Notes
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Question #3 (medium): number of terms in the series needed to meet the error bound. Alternating series test states that the series converges if it meets two conditions: , it can be written as a more obvious alternating series like: for all. After the series turns out to be convergent, then the number of terms needed for series to be within the assigned error bound can be calculated based on | | | | First the series needs to be proven to be convergent. Since it is an alternating series, it can be put against the alternating series test, which requires meeting two of the conditions. , so which is without the alternating factor so it meets the first condition. Then to determine how many terms are needed for the sum to be within the given accuracy: try the first few "s. Since it is outside the error bound, then test the next one:
