Alternating Series and Intervals of Convergence
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Name:
Show all work.
#1(2 pts) Find a power series with interval of convergence [ 1, 3) . No work necessary.
#2(5 pts each) Determine whether the following series converge absolutely, converge
conditionally, or diverge. Show all work and explain all steps thoroughly.
(1) k 2k
a. 
k2
k 1


b.
 (1)
k 1
k
1
sin  
k

#3(2 pts each) Given that S ( x)   ak ( x  2) k converges for x  5 and diverges for x = 2 ,
k 1
determine whether each of the following statements must be true, may be true, or must be false.
Give a brief explanation:
a. The radius of convergence is S ( x ) is 5.
b. The series diverges at x  6 .
c. The interval of convergence for S(x) is [5,1] .
d. The series converges absolutely on the interval ( 5,1) .
ln(k )  ( x  3)k
#4(6 pts). Determine the interval of convergence of the power series 
. Show all
k 2  2k
k 1
work and explain all steps thoroughly.

(1) k 2k
converges. If S8 is used to approximate the value of this

k2
k 1
series, will the error be less 0.01? Explain your analysis clearly.

#5(5 pts). The series
#6(3 pts) Find the set of all x 
(1) k  3k
converges.

k
2
k 1 x  k

such that the series