Math 262 Equation Sheet
INFINITE SEQUENCES
Review Let and
f ( x) =
ak .
a1 + a 2 a3 + a 4 .
If the function is The series converges if and only if 1. a k +1 a k ; the series is decreasing, and 2. Ratio Test Absolute
Convergence
cfw_a n be a sequence. If
MATH 262: Sample Final with Solutions Problem 1. Determine the values of x for which the series
n=1
(4x + 1)n n
converges absolutely, converges conditionally, or diverges. Solution. Apply the Ratio Test. (4x + 1)n+1 (4x + 1)n (4x + 1)n+1 n n / = |4x + 1|
Sample Final Examination 1. For each of the following series nd (i) the radius of convergence and (ii) what happens at the endpoints of the interval of convergence. (a) (1)n x2n , n4n n=1
(b)
x3n . 64n n + 1 n=0
2. (a) Find the Maclaurin series of F (x) =