1. ## [SOLVED] Power Series(Radius and interval of convergence)

hey there.. i hope u guys can help me..
the question is...
Determine the interval and radius of convergence of the power series below..
$\displaystyle \sum\limits_{k=0}^\infty$k!(x-3)^k

then..
c - r < x < c + r
3 - 0 < x < 3 + 0
hence, x = 3

when x = 3..
$\displaystyle \sum\limits_{k=0}^\infty$k!(3-3)^k = 0

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

2. Originally Posted by nameck
hey there.. i hope u guys can help me..
the question is...
Determine the interval and radius of convergence of the power series below..
$\displaystyle \sum\limits_{k=0}^\infty$k!(x-3)^k

then..
c - r < x < c + r
3 - 0 < x < 3 + 0
hence, x = 3

when x = 3..
$\displaystyle \sum\limits_{k=0}^\infty$k!(3-3)^k = 0

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

Well, the interval of convergence could be put as $\displaystyle \{3\} = [3,3]$ , but I guess that depends on the teacher's taste. At any rate, 0 is not an interval but a single number.

Tonio