Question

$\frac{1}{n^s}-\int_n^{n+1} \frac{\mathrm{d}t}{t^s} \leq \frac{s}{n^{s+1}}$ looking for different proof

score 46 · Answer 1 · 2026-03-25 13:57:06

46

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$\frac{1}{n^s}-\int_n^{n+1} \frac{\mathrm{d}t}{t^s} \leq \frac{s}{n^{s+1}}$ looking for different proof

Published on 25 Mar 2026 - 13:57

score 22 · Answer 2 · 2018-10-30 17:13:37

22

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Show that $|(f + t_1g)(f + t_0g)| \ge ( |f| - |g| )^2.$

Published on 30 Oct 2018 - 17:13

score 66 · Answer 3 · 2018-10-30 17:22:56

66

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proving the inequality $\frac{1}{\sqrt[n]{1+m}}+\frac{1}{\sqrt[m]{1+n}}\ge 1$

Published on 30 Oct 2018 - 17:22

score 19 · Answer 4 · 2026-04-02 04:53:47

What is needed for the inequality $c_1\cdot r^n \le f(r,n) \le c_2\cdot r^n$ to imply that $f(r,n)$ is of the form $c\cdot r^n$?

score 106 · Answer 5 · 2026-03-29 00:06:41

106

Views

Concrete mathematics exercise 1.17 upper bound intuition

Published on 29 Mar 2026 - 0:06

score 59 · Answer 6 · 2026-04-03 23:19:59

59

Views

$|d(x,A)-d(x,B)|\le d(x,y)$

Published on 03 Apr 2026 - 23:19

score 983 · Answer 7 · 2018-10-31 02:59:17

983

Views

Is the following proposition, "If $x < y$, then $x \leq y$" true or false?

Published on 31 Oct 2018 - 2:59

score 409 · Answer 8 · 2026-03-26 13:01:45

409

Views

Which inequality for the fourth central moment do we need to apply here?

Published on 26 Mar 2026 - 13:01

score 54 · Answer 9 · 2018-10-31 10:35:40

54

Views

Given $0\leq \beta\leq \tau\leq 1$, prove $e^\beta - 1\leq (1+\tau)\beta$ and $1-e^{-\beta}\geq (1-\frac{\tau}{2})\beta$

Published on 31 Oct 2018 - 10:35

score 3.7k · Answer 10 · 2018-10-31 17:43:17

3.7k

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Does cross multiply always work for inequalities if both denominators are both positive or negative

Published on 31 Oct 2018 - 17:43

score 55 · Answer 11 · 2018-10-31 23:00:44

55

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Determine the set of all $x∈ℝ$ satifying $x^2 + |x-1| ≤ 1$

Published on 31 Oct 2018 - 23:00

score 66 · Answer 12 · 2026-04-04 00:56:46

66

Views

$d(A,B) \le d(x,A) + d(x,B)$

Published on 04 Apr 2026 - 0:56

score 71 · Answer 13 · 2018-11-01 07:39:11

71

Views

$\frac{1}{4rs}[(r+s)^2\cos \frac{\pi}{2}(r+s)-(s-r)^2\cos \frac{\pi}{2}(s-r)]$ near 0

Published on 01 Nov 2018 - 7:39

score 312 · Answer 14 · 2026-03-28 02:06:42

312

Views

Find the maximum of the value $c(n)$ similar to Hardy's inequality

Published on 28 Mar 2026 - 2:06

score 1.6k · Answer 15 · 2018-11-01 12:05:00

1.6k

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If $x,y,z>0$ and $x+y+z=1$ then $\frac{xyz}{(1-x)(1-y)(1-z)}\le\frac{1}{8}$

Published on 01 Nov 2018 - 12:05

List Question

$\frac{1}{n^s}-\int_n^{n+1} \frac{\mathrm{d}t}{t^s} \leq \frac{s}{n^{s+1}}$ looking for different proof

Show that $|(f + t_1g)(f + t_0g)| \ge ( |f| - |g| )^2.$

proving the inequality $\frac{1}{\sqrt[n]{1+m}}+\frac{1}{\sqrt[m]{1+n}}\ge 1$

What is needed for the inequality $c_1\cdot r^n \le f(r,n) \le c_2\cdot r^n$ to imply that $f(r,n)$ is of the form $c\cdot r^n$?

Concrete mathematics exercise 1.17 upper bound intuition

$|d(x,A)-d(x,B)|\le d(x,y)$

Is the following proposition, "If $x < y$, then $x \leq y$" true or false?

Which inequality for the fourth central moment do we need to apply here?

Given $0\leq \beta\leq \tau\leq 1$, prove $e^\beta - 1\leq (1+\tau)\beta$ and $1-e^{-\beta}\geq (1-\frac{\tau}{2})\beta$

Does cross multiply always work for inequalities if both denominators are both positive or negative

Determine the set of all $x∈ℝ$ satifying $x^2 + |x-1| ≤ 1$

$d(A,B) \le d(x,A) + d(x,B)$

$\frac{1}{4rs}[(r+s)^2\cos \frac{\pi}{2}(r+s)-(s-r)^2\cos \frac{\pi}{2}(s-r)]$ near 0

Find the maximum of the value $c(n)$ similar to Hardy's inequality

If $x,y,z>0$ and $x+y+z=1$ then $\frac{xyz}{(1-x)(1-y)(1-z)}\le\frac{1}{8}$

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