Recent content by PhyzX

Thank you, I understand what the question is asking now. Would you happen to know what these equations might be called so that I can search them up.

I think I don't quite understand the question. My interpretation of ##T(j)|X_0 = j## is that it is equal to the minimum number of steps needed to return to state ##j##. Looking at the transition probabilities I figured that the chain should immediately return to state 0 and then climb back up...

Homework Statement Markov process has probabilities p_{j,j+1} = 1-p_{j,0} = (\frac{j+1}{j+2})^k for j=0,1,2,... If T_j = min[n>1 : X_n=j] What is E[T(j)|X_0=j] for j=0,1,2,...? Homework EquationsThe Attempt at a Solution I figured that T(j)|X_0=j is j+1 but don't know how to work out the...

Hey, yeah I've noticed that. The sequence converges to both 1 and -1 if I'm not mistaken? However I am told to use the method of finding suitable epsilon and N in each case to produce counter examples. So I can't use subsequences and such to show that it converges twice. However I think I've...

Thanks for the link, however I am required to use the contradiction in each case method.

Yes that is the problem, sorry it took so long to get across.

Your guess is correct but it is not a sum, just a sequence. I had a look around and found a similar question albeit slightly simpler: https://www.physicsforums.com/showthread.php?t=491938 I'm struggling to emulate the techniques used in that thread.

Sorry if I wasn't clear. The expression is a sequence starting from 1 through the Natural numbers. n/(n+1) is a factor not part of the exponent. The cases are L<0 L=0 L>0 Where L is the limit of the sequence.

Homework Statement Using a proof by cases, show that (-1)^n * (n/(n+1)) is divergent Homework Equations A sequence a_n is said to be convergent if For every real number ε > 0, there exists a natural number N such that for all n > N, |a_n − L| < ε. The Attempt at a Solution Tried...

Maybe I'm confused at the definition of a snapshot graph. My understanding is that each point on the graph represents a particle's vertical velocity (since waves on a string are transverse) at that position taken at one instance of time. I'm confused on how I would calculate the displacement...

I'm stuck on this question too. Can you explain exactly how you use the 50cm/s as a reference? thanks