# There was a post that was recently voluntarily deleted, but I want to answer it. Can anyone help find it?

There was a question trying to find a closed form solution for,

$$F(n)=\sum_i^n \lfloor i/5 \rfloor$$

I got that for $n$ in the range $[5 \cdot k-6,5 \cdot k-1]$, where $k$ is a positive natural number, the solution is,

$$F_{[5 \cdot k-6,5 \cdot k-1]}(n)=k \cdot n-{1 \over 2} \cdot (7 \cdot k-5 \cdot k^2)$$

Where the subscript limits the domain of $F$. I don't really care about posting the answer, I'd just like the Op of the question to know the solution. If it helps, I believe Thomas Andrews had a partial answer. Ideally, I'd like this information to be passed on to the Op.

• Your browser's history might help. – user147263 Sep 8 '15 at 2:17
• If it's the question Antonio found, I also have something to be passed on to the OP, and it isn't information. What a piece of work! – Gerry Myerson Sep 8 '15 at 5:47
• What an attitude! Do we really want that reopened? I need to commute now, so cannot send in a warning, but, rest assured, one is coming. – Jyrki Lahtonen Sep 8 '15 at 6:09
• This is a new user who apparently has several misunderstandings about how the site works. I addressed a few in a ModMessage. Other moderators may chime in with theirs. Sigh, if only the new users would spend a little while learning the site norms. – Jyrki Lahtonen Sep 8 '15 at 9:23
• @JyrkiLahtonen I agree. Would you mind directing the Op to this page, if (s)he is interested in an answer? – Zach466920 Sep 8 '15 at 14:05
• Don't overlook the option of posting the question you want to answer as a new question. – Hurkyl Sep 8 '15 at 14:30
• @Hurkyl Thanks for the suggestion, I'll try doing that when I have a bit of time. – Zach466920 Sep 8 '15 at 14:45

$$F(n) = \sum_{i=0}^{n} F\left(\left\lfloor\frac{i}{5}\right\rfloor\right),$$
• Thanks. As far as my answer is concerned, each $k$ only gives a solution in a certain range. For instance, for $k=2$ it gives a solution if $4 \le n \le 9$, and $n$ is an integer. – Zach466920 Sep 8 '15 at 14:04