Question

How to simplify $2^{\lceil log_2(n) \rceil} - 2^{\lfloor log_2(n) \rfloor}$?

score 204 · Answer 1 · 2026-02-23 07:44:15

204

Views

How to simplify $2^{\lceil log_2(n) \rceil} - 2^{\lfloor log_2(n) \rfloor}$?

Published on 23 Feb 2026 - 7:44

score 939 · Answer 2 · 2016-11-09 08:05:21

939

Views

How can I solve $T(n) = \lfloor \frac {n} {2}\rfloor + T(\lceil \frac{n}{2} \rceil)$?

Published on 09 Nov 2016 - 8:05

score 299 · Answer 3 · 2016-11-13 00:56:05

299

Views

How to find limit of function: $\lim_{x\to 0}\left(x{{\left\lfloor{ \frac{1}{x}} \right\rfloor}}\right)$

Published on 13 Nov 2016 - 0:56

score 172 · Answer 4 · 2026-03-26 01:26:40

172

Views

Name for Unsolved Problem

Published on 26 Mar 2026 - 1:26

score 109 · Answer 5 · 2016-11-13 22:53:32

109

Views

Show that $\lim\limits_{x \to \infty} \frac{\lfloor x \rfloor}{x} = 1$

Published on 13 Nov 2016 - 22:53

score 54 · Answer 6 · 2016-11-16 04:25:10

54

Views

How to show that $\left\lfloor{N/3}\right\rfloor < \left\lfloor{\left({N + 3}\right)/p}\right\rfloor$ has no solution for $p \ge 5$ where $N \ge p$

Published on 16 Nov 2016 - 4:25

score 70 · Answer 7 · 2016-11-16 08:44:26

70

Views

Is my proof mathematically correct?

Published on 16 Nov 2016 - 8:44

score 104 · Answer 8 · 2026-03-29 16:00:47

104

Views

Prove by induction that Fn denotes the Fibonacci sequence $F_n=\sum_{j=0}^k {n-j \choose j} \text{ where k=}\left\lfloor\frac n2\right\rfloor$

Published on 29 Mar 2026 - 16:00

score 116 · Answer 9 · 2016-11-17 06:41:45

116

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$ \lim_{x \rightarrow \pi}\left \lfloor \frac{3\sin(x^2)-1}{2\cos(x)+1} \right \rfloor$=?

Published on 17 Nov 2016 - 6:41

score 187 · Answer 10 · 2026-03-25 17:20:01

187

Views

Solve $\frac{1}{\left\lfloor{x}\right\rfloor}+\frac{1}{\left\lfloor{2x}\right\rfloor}=\{x\}+\frac13$

Published on 25 Mar 2026 - 17:20

score 98 · Answer 11 · 2026-03-25 19:25:18

98

Views

Analyzing the continuity of $\sin(x\left \lfloor{\frac{\pi }{x}} \right \rfloor)$ at 0

Published on 25 Mar 2026 - 19:25

score 483 · Answer 12 · 2016-11-19 12:52:12

483

Views

$\lfloor a n\rfloor \lfloor b n\rfloor \lfloor c n\rfloor = \lfloor d n\rfloor \lfloor e n\rfloor \lfloor f n\rfloor$ for all $n$

Published on 19 Nov 2016 - 12:52

score 42 · Answer 13 · 2016-11-20 14:46:11

Let $f:\mathbb{R} \to \mathbb{R}$ be a function, so that $f(x)=\lfloor{2\lceil{\frac x2}\rceil}+\frac 12 \rfloor$. How do I find $f([-4,-2])$?

score 37 · Answer 14 · 2016-11-23 00:44:29

37

Views

Guidance with a floor function proof

Published on 23 Nov 2016 - 0:44

score 294 · Answer 15 · 2016-11-24 12:13:20

294

Views

Solving an inequality involving floor.

Published on 24 Nov 2016 - 12:13

List Question

How to simplify $2^{\lceil log_2(n) \rceil} - 2^{\lfloor log_2(n) \rfloor}$?

How can I solve $T(n) = \lfloor \frac {n} {2}\rfloor + T(\lceil \frac{n}{2} \rceil)$?

How to find limit of function: $\lim_{x\to 0}\left(x{{\left\lfloor{ \frac{1}{x}} \right\rfloor}}\right)$

Name for Unsolved Problem

Show that $\lim\limits_{x \to \infty} \frac{\lfloor x \rfloor}{x} = 1$

How to show that $\left\lfloor{N/3}\right\rfloor < \left\lfloor{\left({N + 3}\right)/p}\right\rfloor$ has no solution for $p \ge 5$ where $N \ge p$

Is my proof mathematically correct?

Prove by induction that Fn denotes the Fibonacci sequence $F_n=\sum_{j=0}^k {n-j \choose j} \text{ where k=}\left\lfloor\frac n2\right\rfloor$

$ \lim_{x \rightarrow \pi}\left \lfloor \frac{3\sin(x^2)-1}{2\cos(x)+1} \right \rfloor$=?

Solve $\frac{1}{\left\lfloor{x}\right\rfloor}+\frac{1}{\left\lfloor{2x}\right\rfloor}=\{x\}+\frac13$

Analyzing the continuity of $\sin(x\left \lfloor{\frac{\pi }{x}} \right \rfloor)$ at 0

$\lfloor a n\rfloor \lfloor b n\rfloor \lfloor c n\rfloor = \lfloor d n\rfloor \lfloor e n\rfloor \lfloor f n\rfloor$ for all $n$

Let $f:\mathbb{R} \to \mathbb{R}$ be a function, so that $f(x)=\lfloor{2\lceil{\frac x2}\rceil}+\frac 12 \rfloor$. How do I find $f([-4,-2])$?

Guidance with a floor function proof

Solving an inequality involving floor.

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