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nothing much. I'm not so great at latex but trying to get better. thanks.


Aug
21
comment radius of convergence for $\sum_{n=1}^{\infty} \frac{z^{n} n^{n}}{n!}$ and $\sum_{n=1}^{\infty} z^{n!}$
@rehband: gotcha. and it seems that besides applying the root test to the whole expression you can also do the limsup thing on the whole expression also. now I understand A) and B). your explanation is really appreciated.
Aug
20
comment radius of convergence for $\sum_{n=1}^{\infty} \frac{z^{n} n^{n}}{n!}$ and $\sum_{n=1}^{\infty} z^{n!}$
@copper: I understand what you and rehband both did for A). It's clear now. For B), I think you are applying the same formula to the series terms themselves when I thought the theorem applied to the $a_n$ coefficient multiplying the $z^{n}$ term. Could one of you clarify what the logic is there ? Thanks.
Aug
20
comment radius of convergence for $\sum_{n=1}^{\infty} \frac{z^{n} n^{n}}{n!}$ and $\sum_{n=1}^{\infty} z^{n!}$
I'm printing out and will study answers and see if I follow. If I do, I will check off. Otherwise, I'll explain what I don't understand. thanks to all.
Aug
20
asked radius of convergence for $\sum_{n=1}^{\infty} \frac{z^{n} n^{n}}{n!}$ and $\sum_{n=1}^{\infty} z^{n!}$
Aug
20
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
adam: thanks for explaining. no. it was my mistake. definitely your answer was great. I think I even get the concept of it converging on a different disk now, thanks to you.
Aug
19
asked Check my answer for find a formula for $\sum_{n=0}^{\infty} \frac{z^{n}}{4^{n+2}}$
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
@adam: is it correct to say that both series are converging to the function $\frac{1}{1-z}$, but A) the series expanded about $5i$ converges to $\frac{1}{1-z}$ where the center of the disk is (0,5i) and B) the series expanded about $0$ converges to $\frac{1}{1-z}$ where the center of the disk is the point $(0,0i)$. thanks.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
@adam. I will ponder your wisdom some more. and your help and patience is really appreciated. one more bother: is what you said above only true for complex series or series in general. thanks a lot.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
my confusion is that $\frac{1}{1-z}$ can be expanded about the point $z = 0$ or $z = 5i$. doing this results in two different series even though the function in both cases is $\frac{1}{1-z}$. Adam explained that the function is on two different "sets" so I'm trying to ponder that. thanks for any insight on my difficulty.
Aug
18
accepted where does $\frac{1}{1-z}$ about the point $5i$ converge.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
adam: I checked your answer now also but I'm not sure if it's allowed to do it later. if it doesn't stick, then my apologies.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
hi adam: not at all. I usually check all of them and meant to this time also. is there some etiquette about only checking one or it okay to check them all if you like them all ? all of youir answers were tremendous. i just still need to ponder the last part about a "different set". thanks again.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
thanks adam. I had a typo in my question. I meant $\frac{1}{1-z}$. I'm gonna print out your wisdom and the other people's and go over carefully. this stuff definitely makes me play twister with my brain.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
@Adam: If it's not simple, don't worry about it but $\frac{1}{z} = \frac{1}{1-5i -(z-5i)}$ so how can the same series converge on two different disks at the same time ? It might be obvious to most but not to me. thanks.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
hi adam: last bother. is the one that the answer was done for ( not mine. the right one ), a disk centered at the point in the complex plane (0,5i) ? thanks.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
Thank you. I read the answers and one question I have is: since the series being expanded is 1/z what does it really mean to expand the series about the point 5i. to me the expansion is equivalent to the expansion about z = 0 since we subtracted and added 5i.thanks.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
I wrote my comment in the wrong place so in case some missed it, I will write it again.
Aug
18
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
I read the answers and one question I have is: since the series being expanded is 1/z what does it really mean to expand the series about the point $5i$. to me the expansion is equivalent to the expansion about z = 0 since we subtracted and added 5i.thanks.
Aug
17
comment where does $\frac{1}{1-z}$ about the point $5i$ converge.
thanks to all. I'm going to print out and read carefully since I clearly did the wrong thing. I will check all of the answers since they are all extremely useful. it's much appreciated.
Aug
17
asked where does $\frac{1}{1-z}$ about the point $5i$ converge.