# algorithms – The interperation of expected time bound for searches in a hash table

As CLRS book,page 260 stated,

Thus, the total time required for a successful search is $$Theta{left(2+alpha/2-alpha/2nright)}=Theta{(1+alpha)}$$

I wouldn’t have any problem if the author says the bound is eventually $$Theta{(2+alpha/2-alpha/2n)}$$ or even $$Theta{(1+alpha(1-frac{1}{n}))}$$. What kind of logics shall we apply to simplify the original result, i.e, cancelling the factor $$1/n$$ of $$alpha$$. What i’ve missed? is anyone got the same confusion?