Power Series(Radius and interval of convergence)

[naspek]

hey there..
i've try this question(attachment) already...
i got radius of convergence, R = 1/8

at x = 1/8,
converges...

at x = -1/8
i don't how to do this one..
please help me..

 

[Dick]

How did you conclude that has radius of convergence 1/8?? Your bmp has an n! in the denominator. What does the ratio test tell you?

 

[naspek]

How did you conclude that has radius of convergence 1/8?? Your bmp has an n! in the denominator. What does the ratio test tell you?

to find the radius, r..
i use an / an+1

 

[Dick]

to find the radius, r..
i use an / an+1

Go ahead. Use it. What the limit of the ratio?

 

[naspek]

then.. i got radius = 1/8

 

[Dick]

then.. i got radius = 1/8

What's the ratio an/an+1? I don't think you are getting that limit right.

 

[naspek]

i've revised back my calculation..
should i get infinity for my radius..

 

[Dick]

i've revised back my calculation..
should i get infinity for my radius..

Yes.

 

[naspek]

ok.. so.. i need to check the interval of convergence..

when x = infinity,
the series will converges..

when c = -infinity,
the series will converges too..

hence, my interval of convergence is (-infinity,infinity)

am i right?

 

[Dick]

It converges for ALL x, that's what you mean, right? There's no such number as +infinity or -infinity. They are only limits you approach. You don't have to check them.

 

[naspek]

alright! i understand now..
Thanks Dick =)