How to express sum of even numbers in sigma notation Given a positive integer number n, how can I express the sum of all positive even numbers up to n in sigma notation?

Given a real number $x$ we can define $\lfloor x \rfloor$ to be the greatest integer less than or equal to $x$. For instance, $\lfloor 3 \rfloor = 3$ and $\lfloor 7.81 \rfloor = 7$.
Thus we can write the sum of even integers less than or equal to $n$ as
$$\sum_{k=0}^{\lfloor n/2 \rfloor} 2k$$
If you stare hard enough at this you'll see why it works: if $n$ is even then $\lfloor \frac{n}{2} \rfloor = \frac{n}{2}$, so the last term is $2 \cdot \frac{n}{2} = n$. If $n$ is odd then $\lfloor \frac{n}{2} \rfloor = \frac{n-1}{2}$, so the last term is $2 \cdot \frac{n-1}{2} = n-1$.
