I was reading Nesterov's famous paper Smooth minimization of non-smooth functions. I got stuck in the first line of Theorem 3's proof. According to the paper, inequality (4.5) should be a direct result from Theorem 2. However I failed to see where $\frac{1}{(N+1)^2}$ in the first term of right-hand side comes from. Shouldn't it be $\frac{4}{(N+1)(N+2)}$?
It should be a simple arithmetic manipulation. But I cannot figure it out after hours of thinking. I hope anyone familiar with this paper could explain it to me. Thanks in advance!
I just skipped (4.5) and read rest of the proof. I found the missing '4' in (4.7), so I guess Nesterov made a typo there.
Hope it could help anyone confused by the same problem :)