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...
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...
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...
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...
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...