MAT136H1 Lecture Notes - Alternating Series Test, Alternating Series
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MAT136H1 Full Course Notes
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Question #2 (medium): converging series against alternating series test. 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. 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 . Test the series against the alternating series test for convergence or divergence. To see if it meets the first condition of the alternating series test, take the first derivative and see if it is negative. Then it is a decreasing function for all n. , therefore it is decreasing ( )[ ( )] for all , Now that it met the first condition, continue to check for the second condition of the alternating series test:
