Right i think I've got it, if I've fudged it or my reasoning is wrong i'd appreciate a correction.
So I've considered it as if it was a particle which has split into two, a photon and the spaceship in motion. I've taken it from the rest frame of the initial space ship. So using...
Hi I'm having trouble with this question and would like some kind of hint on how to proceed.
A photon starship starts from rest and propels itself by emitting photons in the direction opposite to its motion until it reaches a speed v. Use energy momentum conservation law to show that the...
Seems good. Sn>0 for all n, so let M=min{s_0, s_1 ...}. Then as sn converges to s there exists an N such that |sn-s|<eM for all n>N.
\frac{|s_n-s|}{s_n}\leq \frac{|s_n-s|}{M}< e
Yeah, so both cases are sorted.
I think the problem is that we have
log(S_{n}) - log(s) = log(\frac{S_{n}}{s}) \leq \frac{S_{n}}{s} - 1
but we can't say that
|log(S_{n}) - log(s)| = |log(\frac{S_{n}}{s})|\leq |\frac{S_{n}}{s} - 1|
because the last inequality is only true if sn/s>1. If that was the case then we...