List questions from ceiling-and-floor-functions

185

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How would you prove that the sequence $T_n=\left\lfloor \dfrac{T_{n-1}}{3} \right\rfloor + p$ converges after a finite number of iterations?

Published on 16 Sep 2022 - 19:03

217

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How to calculate number of shapes inside a shape

Published on 30 Mar 2026 - 8:01

72

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Simplifying $\sum\limits^n_{i=1}\bigl(\prod\limits^n_{j=1}\bigl(a_j\bigl\lfloor\frac{x_j-x_i}{|x_j-x_i|+1} \bigr\rfloor+1\bigr)\bigr)b_i$

Published on 21 Sep 2022 - 5:44

124

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Continuity at a point vs. interval—contradicton or not?

Published on 21 Sep 2022 - 22:23

69

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Equivalent symmetric sums proof

Published on 27 Mar 2026 - 4:04

28

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Showing that $\lfloor \sqrt{n^2+b}\rfloor=n \iff 0 \le b < 2n+1$

Published on 26 Sep 2022 - 19:17

207

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floor equation for fibonacci sequence

Published on 30 Sep 2022 - 18:27

72

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Floor function equivalence relation and partition

Published on 29 Mar 2026 - 22:25

116

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Solve the equation: $\lfloor{x}\rfloor+\lfloor{2x}\rfloor=\frac{5x-1}{2}$

Published on 07 Oct 2022 - 8:06

161

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Direct vs Contradiction Proof: For any odd integer n, prove that $\lfloor n^2/4 \rfloor = (n^2-1)/4$.

Published on 07 Oct 2022 - 10:32

92

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Prove or disprove: If $a_n$ is Cauchy, is $\lfloor a_n \rfloor$ Cauchy?

Published on 09 Oct 2022 - 19:17

174

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find the smallest n such that $a_n > 2019$

Published on 19 Oct 2022 - 1:10

53

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Drawing floor and ceiling functions

Published on 21 Oct 2022 - 4:18

144

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How to solve this for every integer n, ⌊⌊n/2⌋/3⌋=⌊n/6⌋?

Published on 04 Apr 2026 - 16:16

213

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Combination with repeated floor operations same as the whole combination?

Published on 02 Nov 2022 - 9:53

List Question

How would you prove that the sequence $T_n=\left\lfloor \dfrac{T_{n-1}}{3} \right\rfloor + p$ converges after a finite number of iterations?

How to calculate number of shapes inside a shape

Simplifying $\sum\limits^n_{i=1}\bigl(\prod\limits^n_{j=1}\bigl(a_j\bigl\lfloor\frac{x_j-x_i}{|x_j-x_i|+1} \bigr\rfloor+1\bigr)\bigr)b_i$

Continuity at a point vs. interval—contradicton or not?

Equivalent symmetric sums proof

Showing that $\lfloor \sqrt{n^2+b}\rfloor=n \iff 0 \le b < 2n+1$

floor equation for fibonacci sequence

Floor function equivalence relation and partition

Solve the equation: $\lfloor{x}\rfloor+\lfloor{2x}\rfloor=\frac{5x-1}{2}$

Direct vs Contradiction Proof: For any odd integer n, prove that $\lfloor n^2/4 \rfloor = (n^2-1)/4$.

Prove or disprove: If $a_n$ is Cauchy, is $\lfloor a_n \rfloor$ Cauchy?

find the smallest n such that $a_n > 2019$

Drawing floor and ceiling functions

How to solve this for every integer n, ⌊⌊n/2⌋/3⌋=⌊n/6⌋?

Combination with repeated floor operations same as the whole combination?

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