MAT136H1 Lecture Notes - Geometric Series

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

Document Summary

Question #1 (easy): representing function into power series. To convert the function into a power series, first think of geometric series whose sum is where a is the constant first term and r the ratio. Since a can be taken to outside the summation, ultimately then, the goal is to put into. Then given that geometric series converges for | | , find the value for x which in turn causes the geometric series ratio to be less than . Find a power series representation for the function and determine the interval of convergence. First the above function needs to be put into the geometric series sum form of. Then, then can be taken as the ratio for the geometric series, so: Geometric series converges for | | , thus in this case since , then | | | | for.