Given $a_{n+1}=a_{n}+\frac{1}{a_{n}}$, how can I find $\lfloor a_{1000} \rfloor$?
36514
Show that $45<x_{1000}<45.1$
79182
what is the limit of $\displaystyle \lim_{x\to 0} \frac{x}{a}\cdot \lfloor{\frac{b}{x}\rfloor}$
97656
Finding $a_n$ if $a_0=a_1=1,a_{n+1}=n(a_n+a_{n-1})\ \ (n\ge 1).$
142338
Prove that $\lfloor\frac{n+1}{2}\rfloor+\lfloor\frac{n+2}{4}\rfloor+\lfloor\frac{n+4}{8}\rfloor+\lfloor\frac{n+8}{16}\rfloor+ \dots=n$
124426
Help in evaluating: $\lim_{n \to \infty} \frac{\sum_{k=1}^n\lfloor kx\rfloor}{n^2} $
114228
Find the number of solutions to $ \lfloor x \rfloor + \lfloor 2x \rfloor + \lfloor 4x \rfloor + \ldots + \lfloor 32x \rfloor =12345$
30639
Efficient computation of $\sum_{k=1}^n \left\lfloor \frac{n}{k}\right\rfloor$
70354
Find the sum of all the multiples of 3 or 5 below 1000
30414
Prove using combinatorics $\sum\limits_{k=0}^n 2^k \binom{n}{k} \binom{n-k}{\lfloor{\frac{n-k}{2}}\rfloor}=\binom{2n+1}{n}$
38811
Solutions to $\frac1{\lfloor x\rfloor}+\frac1{\lfloor 2x\rfloor}=\{x\}+\frac13$
1715
Proof: How many digits does a number have? $\lfloor \log_{10} n \rfloor +1$
111665
How prove this $\{a\}\cdot\{b\}\cdot\{c\}=0$ if $\lfloor na\rfloor+\lfloor nb\rfloor=\lfloor nc\rfloor$
143306
Limit involving floor function: $\lim\limits_{x\to 0} x \left\lfloor\frac1x \right\rfloor$
101641
Induction with floor, ceiling $n\le2^k\implies a_n\le3\cdot k2^k+4\cdot2^k-1$ for $a_n=a_{\lfloor\frac{n}2\rfloor}+a_{\lceil\frac{n}2\rceil}+3n+1$
92557
If the $n^{th}$ partial sum of a series $\sum a_n$ is $S_n = \frac{n-1}{n+1}$, find $a_n$ and the sum.
82803
Prove that $\lfloor\lfloor x/2 \rfloor / 2 \rfloor = \lfloor x/4 \rfloor$
13098
Find a formula for $\sum\limits_{k=1}^n \lfloor \sqrt{k} \rfloor$