In a simple uniform hashing with chaining collision, the time complexity of a successful search is: $Θ(1 + (1 + \frac{α}{2} - \frac{α}{2n}))$ where $α=\frac{n}{m}$, but I don't understand how to determine it.
I tried to calculate the cost of access of each node in the list and to divide it by the number of elements of the list, but it doesn't seem correct. $$1+\frac{m}{n}\cdot \sum _{i=0}^{\frac{n}{m}}\frac{n}{m}-i=1+\frac{n+m}{2m}$$