Linear multistep method (numerical analysis) ODE's

I've managed to show it is zero stable and not consistent, and that it is not convergent because zero-stable + consistent = convergent. Now I'm stuck with the part bracketed in red. How would I choose tau and find a general solution for U^n?

Do I just take tau=1/N and so then N=1/tau?

For the general solution for U^n I tried doing:

U^0 = 0

U^1 = tau/3

U^2 = U^1 (from the 1st equation, left hand side) = tau/3

U^3 = U^2 = tau/3

...

U^n = (n/n) tau/3. Is this correct?

Many thanks!

By the way, how would I go about showing the limit as required in the question?

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You can write formulas here by including $\TeX$ code in dollar signs, for instance $\lim_{\tau\to0}U^N\ne u(1)$. You may find people are more willing to answer your question if you make the formulas more easily readable. If you don't know how to write something in $\TeX$, you can look around the site; you can right-click on any formula you see and select "Show Source" to see the $\TeX$ code for it. – joriki Nov 7 '11 at 9:02
Alright thanks, i will try to look at it soon! – John Southall Nov 7 '11 at 21:25