L thtmledopislauuspiayiurhhhrglmsumofmiumh series?
journals The molmiulidtasaiesisrbfredasmlimiofmseqnemeofpalmlfmlimitofdlisseqneuee
domrtntexisl. tin series issaidhdiverga.
2. What is the sum of the following innite series?
+1+ 1 + l + 1 +
4 8 [IS 32
We can take derivatives and integrate term by term. No more interval of convergence information, onlyr radius.
E Theorem If the power series 2 12,12: a)" has radius of convergence R > 0,
then the function f dened by
Examples of Modeling Problems:
Newtons law of cooling states that the temperature of an object changes at a rate propor-
tional to the difference between the temperature of the object itself and the temperature
of its surroundings (the ambient air tempera
Improved Limit Comparison
THEOREM Limit em = ' on Test Suppose: that an :2: 0 and b" :v e for
all n a N (N an integer).
1. If lim & = c 9 0, then 2:1, and Eb" both converge or both diverge.
2. If lim = 0 and 25, converges, then Zen converges.
Using Mathematiea for Stream Plots cfw_Similarte a Direction Field er Slope Field]
Mice Field and Owls Example from Lecture
H111: Strenlnnsitlmnti: [1, 45 - .5 3-, ft, .5, 9, cfw_3" 895, 9H5, limesp Ernie]