MAT136H1 Lecture Notes - Alternating Series Test, Alternating Series

• School: UTSG
• Department: Mathematics
• Course: MAT136H1
• Professor: all

Document Summary

Question #5 (medium): making the alternating series convergent. To find the missing variable to make the alternating series convergent, keep the missing variable and test against two conditions of the alternating series test, then work backward to find the suitable value for that makes the series convergent. In order for the alternating series to be convergent, it needs to pass two criteria of the alternating series test conditions. For the first condition, take the first derivative and see which value makes the derivative negative for all : As for the first term in the numerator ( ) this is also positive since . To meet both conditions, then which includes this is negative when.