Radius and interval of convergence for ∑k!(x-3)^k

[naspek]

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

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

 

[HallsofIvy]

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

 

[naspek]

Got it! Thanks! =)