<p>Can anyone please solve this sequence and give me the formula?
0,1,1,2,2,3,3,4... every positive integer is repeated.</p>
<p>If it's any help, I got as far as n/2 for even numbers and (n/2)-(1/2) for odd numbers? And every successive number differs by +/- 1/2, as in (n/2)-(1/2), (n/2)-(-1/2)+(1/2), (n/2)-(1/2)+(1/2)-(1/2) and so on.</p>
<p>floor(n/2)</p>
<p>What does this mean?</p>
<p>Divide n by two and truncate</p>
<p>At the risk of sounding very very stupid: truncate what? And what exactly is truncate because I only have a very slight idea?</p>
<p>Okay, I got it. I’m sorry, we use a different terminology here, so I was confused for a second. Truncate would be the ceiling function, right? But the floor function would apply here, no?</p>
<p>Truncating and the floor function (and the greatest integer function, if you use that terminology) are the same.</p>
<p>Another question (sorry, I have a calculus exam tomorrow and there’s a lot of last minute cramming):
I need to make this converge to 1/2,</p>
<pre><code> ((n^2 - n)^1/2) - n
</code></pre>
<p>What I’m doing is completing the square in the underroot. So I get ((n-1/2)^2 - (1/2)^2)^1/2 -n. I then discard the (1/2)^2 because I’m taking (n-1/2)^2 to be equal to infinity and (1/2)^2 becomes negligible in comparison. Is this legit? As in, does this stand? Because I can’t find any other way to make it converge to 1/2.</p>