Recent content by benf.stokes

Hmm, i see it now. I was confusing norms. Thanks for the help!

Hmm, if f(1)\neq 0 then f(t)-f_n(t) \neq 0 in a open interval around one. But shouldn't it be possible to have a f_n as close as possible to f(t) until 1-1/n say and then decrease linearly to zero? I know this function in particular is discontinuous in the n to infinity limit but can you give...

Homework Statement Let H= C[-1,1] with L^2 norm and consider G={f belongs to H| f(1) = 0}. Show that G is a closed subspace of H. Homework Equations L^2 inner product: <f,g>\to \int_{-1}^{1}f(t)\overline{g(t)} dt The Attempt at a Solution I've been trying to prove this for a...

I figured it out due to your help. Thanks :)

Homework Statement I can't figure out why there is no bound current in the problem 6 (very subtle hint boldfaced) is the pdf below: http://astronomy.mnstate.edu/cabanela/classes/phys370/homework/ps10.pdf Can anybody give me a hint as to why there should be no bound current The Attempt at a...

Hi, Thanks for the help :). I managed to do it

Hi, In griffith's "Introduction to Electrodynamics" he indicates that a specific infinite series has a truncated form (the series and truncated form are given below) And he says the reader can try to show that it indeed has that form...

Thanks for everything . One last thing though: how should I do the comparison so that it's less sloppy?

f(n)=\frac{n^2+2*n+6}{n*(n+1)*(n+2)}=\frac{n+1}{n*(n+2)}+\frac{5}{n*(n+1)*(n+2)} > \frac{n+1}{n*(n+2)}>\frac{1}{n} and thus by the comparison test the series diverges?

Sorry. I misread your post. It is indeed zero. How then is this rewriting useful? f(n) is always positive and the ratio test is useless as it gives r=1

lim n tend to infinity of f(n) is different from zero and thus the series does not converge?

Homework Statement The problem asks you if the series: 1+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+\frac{1}{5}-\frac{1}{6}... converges or diverges Homework Equations The Attempt at a Solution I tried to apply the Leibniz rule but I realized it can't be applied. Is there a transformation of this...

Linear Algebra Hi, I'm just finishing my semester of linear algebra. And as my course is quite applied i feel like I'm missing a big part of linear algebra. And so for Christmas I pretend to order a more theoretical and challenging linear algebra book for self-study. My question is: should I...

Thanks for the reply. Would F(x) = sqrt(x)/(x^2+1) be an acceptable function then?

Homework Statement Let (xn) n ∈ N, be a succession. Construct a function F: [0,plus infinity[ to Rn (if possible continuous) whose restriction to the naturals is (xn) n ∈ N, ie xn = F (n) for all n ∈ N, and such that ∃ limx → + ∞ F (x) = L if and only if ∃ Limn → + ∞ xn = L The Attempt at a...