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Nov
19
comment Examination of convergence of a few series
After a break I will work through your comments and rethink my ideas. Thanks for your effort.
Nov
19
comment Examination of convergence of a few series
Concerning 5 I do not understand what you mean by saying the $k$-th term is positive - shouldn't that include something like "for every even k"? Furthermore does that mean the series does not converge absolutely?
Nov
19
comment Examination of convergence of a few series
@ThomasAndrews: $$\frac{1}{k+3+2/k}\geq \frac{1}{2}$$.
Nov
19
comment Examination of convergence of a few series
@ThomasAndrews: Does $1/2$ suffice?
Nov
19
comment Examination of convergence of a few series
@ThomasAndrews: Would it be correct to remove the sums and to just look at the sequences rather than the series?
Nov
18
comment Cauchy product and the exponential function
Thank you so much - you do help me every time!
Nov
18
comment Cauchy product and the exponential function
WolframAlpha showed me that I should get $1/2\sin(2x)$ as a result, however the $4^n$ makes it difficult to derive the fact that I have to get $(2x)^{2n+1}$ and the $1/2$ in front of everything. This is what I want to know right now.
Nov
18
comment Cauchy product and the exponential function
@BrianM.Scott: I have made another approach, may I ask you to have a look at it?
Nov
17
comment Cauchy product and the exponential function
@BrianM.Scott: Now I do understand this - do you have a hint (rather than the solution ;) ) for the second series for me?
Nov
17
comment Cauchy product and the exponential function
@BrianM.Scott: But you have $\sum_{n\ge 0}\frac{2^n}{n!}=(e-1)^2$ and that confuses me.
Nov
17
comment Cauchy product and the exponential function
@BrianM.Scott: I have a question. Your first result is $(e-1)^2$ but I think it should be $e^2$, shouldn't it?
Nov
17
comment Cauchy product and the exponential function
Thanks I will have a look at that now. @Cocopuffs: I think the indexes should start at 0 so I wrote an email to our TA but nevertheless I can learn that the hard way.
Nov
17
comment Polar coordinates - issue with direction denoted by angle
Actually I don't know, but now it seems comprehensible what you said.
Nov
15
comment Is a statement concerning the future part of a decidable problem?
@ThomasAndrews: Ah ok, one last question - is there any yes/no question which is NOT decidable?
Nov
15
comment Is a statement concerning the future part of a decidable problem?
@ThomasAndrews: What about a scenario where the monitored process will last infinite long?
Nov
14
comment Is this language and its complement is Context free Language?
@BrianM.Scott: I know that - my first answer was quite messy and everything is now... yeah. Thanks for the remark.
Nov
14
comment LaTeX help - multiple answers using set bracket / cases
@Vafa: You are absolutely right and I suggest this to the OP, too. However we could argue that the OP wants to know about MathJaX ;)
Nov
14
comment LaTeX help - multiple answers using set bracket / cases
@Dexter: You're welcome. I have added a link to a good example in my answer. Please have a look.
Nov
13
comment Is there a subset of a non regular language that is regular
@user34790: Every finite language is regular because you can create a enumerate all elements extensionally. Furthermore there exists a regular expression of the form "word1 | word2 | ... | wordN" which implies the regularity of all finite languages.
Nov
13
comment Is there a subset of a non regular language that is regular
I can provide a cheat sheet from my "Theoretical Computer Science" course (in German). Just have a look at the top picture with all the boxes. From top to bottom (on thr right hand side) the descriptions are: all languages $\Sigma^*$, semi-decidable (Type 0), decidable, LOOP-decidable, NP, P, context free (Type 2), regular (Type 3), finite. Hope this might help :)