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Power Series(Radius and interval of convergence)

  • Thread starter naspek
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  • #1
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hey there.. i hope u guys can help me..
the question is...
Determine the interval and radius of convergence of the power series below..
[tex]\sum\limits_{k=0}^\infty[/tex]k!(x-3)^k

i've already find the radius, r = 0
then..
c - r < x < c + r
3 - 0 < x < 3 + 0
hence, x = 3

when x = 3..
[tex]\sum\limits_{k=0}^\infty[/tex]k!(3-3)^k = 0

so.. the interval of convergence is 0
am i do it right?
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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hey there.. i hope u guys can help me..
the question is...
Determine the interval and radius of convergence of the power series below..
[tex]\sum\limits_{k=0}^\infty[/tex]k!(x-3)^k

i've already find the radius, r = 0
then..
c - r < x < c + r
3 - 0 < x < 3 + 0
hence, x = 3

when x = 3..
[tex]\sum\limits_{k=0}^\infty[/tex]k!(3-3)^k = 0

so.. the interval of convergence is 0
am i do it right?
No, the interval of convergence is an interval- a set of points, not a number. Since the radius of convergence is 0, the "interval" of convergence is the single point {3}
 
  • #3
181
0
Got it!!! Thanks!! =)
 

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