Summand Evaluation Help I'm a student currently in an algorithms and data structures class, and my Calculus is unfortunately quite shaky when it comes to summations. As such, I'm struggling to evaluate one of the sum that has appeared in my homework. I was wondering how to go about evaluating it?
Question from Homework:
"Suppose that we use an open-addressed hash table of size m, to store n $\le$ m/2 items. Assume uniform hashing. Let the random variable X denote the number of probes required by the i th insertion. You previously proved $P(X>2logn)=O(1/n^2)$. Now prove that $P(X>2log n )=O(1/n)$.
Currently, I'm sitting with the sum $P(X...)=\sum\limits_{m=0}^{n/2}(m/n)^{2log(n)}$.
Where do I go from here? Thank you in advance!

Hint: for every term in the sum we have $\frac{m}{n} \le \frac{1}{2}$, and there are $\frac{n}{2}+1 = O(\frac{n}{2})$ terms in total. Can you upper bound the sum by $c \cdot \frac{1}{n}$ for some constant $c>0$?
