Recent content by linuxux

Ahhh! Thanks!

Hey people, A little question. I know France has trains running from Paris to London England. I was wondering if anyone knew if that train uses some type of underground tunnel or if it uses a bridge and what the name of it is? I've tried looking for it but its a difficult subject to...

damn. i handed in my assignment saying there were four.

yeah, I've been working on some more. i didn't understand the concept at first. so far i have 4, but i think that's it.

Is there only one?

changed, and what is baby rudin?

Hello. This is the presented problem: Suppose (b_{n}) is a decreasing satisfying b_{n}\ge\ 0. Show that the series \sum^{\infty}_{n=1}b_{n} diverges if the series \sum^{\infty}_{n=0}{2^{n}b_{2^{n}}} diverges. I've already proved that i can create \sum^{\infty}_{n=0}{2^{n}b_{2^{n}}} from...

Thanks.

I'm presented with this, (1)\ (\bigcup^{\infty}_{\n=1}A_{n})^{c}\ =\ \bigcap^{\infty}_{\n=1}A_{n}^{c} and asked why induction cannot be used to conclude this. Now, i know the principle behind induction is to show that P(S)=N by showing that when (i) S contains 1 and (ii) whenever S...

Well, the book was introducing double sums, and at one point it defined the "rectangular partial sums": s_{mn}\ =\ \sum^{m}_{i=1}\sum^{n}_{j=1}a_{ij},\ for\ m,n\ \in\ N. And before it defined t_mn, it said "in the same way that we define the 'rectangular partial sums' s_mn above, define t_mn...

I'm just don't get this question. from my text: define\ t_{mn}\ =\ \sum^{m}_{i=1}\sum^{n}_{j=1}|a_{ij}|, [a_{ij}\ is\ a\ doubly\ indexed\ array\ of\ real\ numbers.] (a)\ prove\ that\ the\ set\ \{t_{mn}\ :\ m,n\ \in\ N\}\ is\ bounded\ above. (b)\ use\ (a)\ to\ conclude\ that\ (t_{nn})\...

thats what I'm thinking. i am actually using the first version of a book that is now in its 8th revision, so I'm guessing there are a few errors. however i saw similar question in another book which did specify a_n and b_n being positive & decreasing sequences, while their series were...

thats not the first time I've come across a flawed question like this. ...thanks anyway.

100% sure.

Infinite Series (2 diverge --> 1 converge) I've been trying to figure this question out: Find examples of two positive and decreasing series, \sum a_n and \sum b_n , both of which diverge, but for which \sum min(a_n,b_n) converges. It doesn't make any sense to me that any positive and...