MAT 21C Lecture Notes - Lecture 8: Limit Comparison Test, Root Test, Ratio Test
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Document Summary
Definition: type of series useful when working with taylor series (will be covered in the future) Form: c n x n = c 0 + c 1 x + c 2 x 2 + c r x r, c n (x-a) n = c 0 + c 1 (x-a) + c 2 (x-a) 2 + c r (x-a) r. Power series always start with n = 0. This means some summations may have to be rewritten to get the desired form. Notice that power series are functions of x, unless the previously studied series. Converges: x = 0, x = a. Practice problems for applying the tests: ((-1) n (n+1)! )/(n!2 n ) -1*2/(2*1) + 6/(2*4) + -24/(6*8) + . Ratio test is appropriate here because factorials are involved: (-1)(n+1)/2 n - + 2/4 - + 4/16 - .
