Question

Show $ f(m) = \left( 1 - \frac{1}{m^2} \right)^{m(m-1)/2} $ is lower-bounded by $\frac{1}{2}$ for $m \ge 1$

score 80 · Answer 1 · 2017-11-11 18:48:40

80

Views

Show $ f(m) = \left( 1 - \frac{1}{m^2} \right)^{m(m-1)/2} $ is lower-bounded by $\frac{1}{2}$ for $m \ge 1$

Published on 11 Nov 2017 - 18:48

score 134 · Answer 2 · 2017-11-13 07:11:58

134

Views

$(x_n)$ be bounded, and $A=\{ x_n\ |\ n\in \mathbb{N}\}.$ If $A$ has only one accumulation point, say x, then $x_n$ is convergent to x.

Published on 13 Nov 2017 - 7:11

score 86 · Answer 3 · 2017-11-14 16:44:02

86

Views

How do you bound the determinant of an $n\times n$ matrix with values $-1, 0, 1$?

Published on 14 Nov 2017 - 16:44

score 106 · Answer 4 · 2017-11-15 09:43:28

106

Views

Reproducible rounding up with hidden constant and known maximum deviation

Published on 15 Nov 2017 - 9:43

score 100 · Answer 5 · 2017-11-15 18:29:47

100

Views

prove that $\inf \{ a^n:n\in \mathbb{N}^* \}=0, 0<a<1$

Published on 15 Nov 2017 - 18:29

score 39 · Answer 6 · 2017-11-15 19:33:01

39

Views

Prove that $\underline\int_{a}^bf\ge0$ when $f(x)\ge 0$

Published on 15 Nov 2017 - 19:33

score 103 · Answer 7 · 2017-11-20 04:20:08

103

Views

Bounds of integration in terms of variable being integrated

Published on 20 Nov 2017 - 4:20

score 50 · Answer 8 · 2017-11-20 16:07:06

50

Views

Covariance/Joint Expectation Calculation

Published on 20 Nov 2017 - 16:07

score 260 · Answer 9 · 2026-03-26 01:18:03

260

Views

Upper bound for the number of representation numbers as the sum of two primes

Published on 26 Mar 2026 - 1:18

score 89 · Answer 10 · 2017-11-21 18:21:35

89

Views

Bounds on number of different-sum subsets

Published on 21 Nov 2017 - 18:21

score 878 · Answer 11 · 2026-03-30 22:42:26

878

Views

How to convert linear inequality constraints into box constraints

Published on 30 Mar 2026 - 22:42

score 133 · Answer 12 · 2017-11-22 11:51:30

133

Views

For which $\lambda$ is $\operatorname{argmin}_b \frac{1}{2}\Vert y-Xb \Vert_2^2+\lambda \Vert b \Vert_1 = 0$?

Published on 22 Nov 2017 - 11:51

score 79 · Answer 13 · 2017-11-24 17:33:08

79

Views

Prove that a sequence is bounded

Published on 24 Nov 2017 - 17:33

score 126 · Answer 14 · 2026-03-28 22:31:04

126

Views

Upper limit for a real gaussian finite sum. Prove $\sum_{i=0}^{N} (2\pi\sigma^2)^{-1/2}e^{-(i+0.5)^2/(2\sigma^2)} < 0.5$?

Published on 28 Mar 2026 - 22:31

score 5.9k · Answer 15 · 2026-03-25 12:54:53

5.9k

Views

Without using a calculator and logarithm, which of $100^{101} , 101^{100}$ is greater?

Published on 25 Mar 2026 - 12:54

List Question

Show $ f(m) = \left( 1 - \frac{1}{m^2} \right)^{m(m-1)/2} $ is lower-bounded by $\frac{1}{2}$ for $m \ge 1$

$(x_n)$ be bounded, and $A=\{ x_n\ |\ n\in \mathbb{N}\}.$ If $A$ has only one accumulation point, say x, then $x_n$ is convergent to x.

How do you bound the determinant of an $n\times n$ matrix with values $-1, 0, 1$?

Reproducible rounding up with hidden constant and known maximum deviation

prove that $\inf \{ a^n:n\in \mathbb{N}^* \}=0, 0<a<1$

Prove that $\underline\int_{a}^bf\ge0$ when $f(x)\ge 0$

Bounds of integration in terms of variable being integrated

Covariance/Joint Expectation Calculation

Upper bound for the number of representation numbers as the sum of two primes

Bounds on number of different-sum subsets

How to convert linear inequality constraints into box constraints

For which $\lambda$ is $\operatorname{argmin}_b \frac{1}{2}\Vert y-Xb \Vert_2^2+\lambda \Vert b \Vert_1 = 0$?

Prove that a sequence is bounded

Upper limit for a real gaussian finite sum. Prove $\sum_{i=0}^{N} (2\pi\sigma^2)^{-1/2}e^{-(i+0.5)^2/(2\sigma^2)} < 0.5$?

Without using a calculator and logarithm, which of $100^{101} , 101^{100}$ is greater?

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