I have came across many books online that all explain that if $N$ is large enough, then the average number of checks in $N/2$ but is there a mathematical explanation or derivation for why this is true?
I have considered when $N=2^n$ and tried to use logarithms but am not getting anywhere with this. Any help would be greatly appreciated
Sorry, I should have made it clear... I was referring to Grover's search algorithm and how I can show that if $N$ is large enough, then the average number of checks is $N/2$. I know I will have to check $N$ objects in the worst-case scenario