$\begingroup$ $(n+1)^3 - n^3 = 3n^2+3n+1$ - so it is clear that the $n^2$ terms can be added (with some lower-order terms attached) by adding the differences of cubes ...

Aug 17, 2015 · So when you get to $1,2,2,3$ this can only go to $1,2,2,3,2,3,3,4$. In the statement of the problem we see $1,2,2,3$ but we don't see the next $4$ numbers, which are …

$$ 1 \rightarrow 1 $$ $$ 2 \rightarrow 2 $$ $$ 3 \rightarrow 2 $$ $$ 4 \rightarrow 3 $$ $$ 5 \rightarrow 3 $$ $$ 6 \rightarrow 4 $$ $$ 7 \rightarrow 4 $$ $$ \vdots $$ $$ 2i \rightarrow i+1 …

I can give you a good approximation if you would prefer: $$\ln(n+1)\le\sum_{i=1}^n\frac1i\le\ln(n)+1$$ This is a rather tight upper limit and lower limit …

One can write $$1+\frac12+\frac13+\cdots+\frac1n=\gamma+\psi(n+1)$$ where $\gamma$ is Euler's constant and $\psi$ is the digamma function. Of course, one reason for creating the …

May 3, 2014 · Users - Comparisons 2 - 1 3 - 3 (+2) 4 - 6 (+3) 5 - 10 (+4) 6 - 15 (+5) 7 - 21 (+6) 8 - 28 (+7) 9 - 36 (+8) I need to be able to take any number of users, and calculate how many …

Apr 28, 2019 · I have been trying to figure out a formula for the sequence: 0, 0, 1, 1, 2, 2, 3, 3, 4, 4 It is not geometric and it is not arithmetic, I tried to apply these ...

Nov 28, 2019 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Sep 30, 2014 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …

Mar 26, 2015 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …