Question

Prove by induction that, for all $n\in\Bbb N$, $\sqrt{n} ≤ \sum_ {k=1}^n \frac{1}{\sqrt{k}} < \sqrt{n} + \frac{n}{\sqrt{n+1}}$.

score 57 · Answer 1 · 2026-04-01 11:05:58

57

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Prove by induction that, for all $n\in\Bbb N$, $\sqrt{n} ≤ \sum_ {k=1}^n \frac{1}{\sqrt{k}} < \sqrt{n} + \frac{n}{\sqrt{n+1}}$.

Published on 01 Apr 2026 - 11:05

score 208 · Answer 2 · 2019-05-22 10:39:30

208

Views

Deriving the information for Cramer-Rao Inequality

Published on 22 May 2019 - 10:39

score 85 · Answer 3 · 2026-03-26 09:19:45

85

Views

Hatcher's proof of proposition (c) for covering spaces

Published on 26 Mar 2026 - 9:19

score 34 · Answer 4 · 2019-05-22 21:24:40

Can anyone elucidate vague hint towards the contradiction of $x^{-1}*x=1$ and $x*0=0$ in $x\in R/0$ $ \implies$ $x^{-1}\in R/0$ in an author's proof?

score 32 · Answer 5 · 2019-05-23 01:30:03

32

Views

Symmetric Operators

Published on 23 May 2019 - 1:30

score 156 · Answer 6 · 2026-04-05 08:08:41

156

Views

Vector spaces are not rigid

Published on 05 Apr 2026 - 8:08

score 65 · Answer 7 · 2019-05-23 19:09:31

65

Views

Tricky proof of inequality

Published on 23 May 2019 - 19:09

score 102 · Answer 8 · 2026-03-28 14:19:35

102

Views

Suppose that the average value on all intervals $[a,b]$ is equal to $f((a+b)/2)$. Prove that $f''(x) = 0$ for all $x \in \mathbb{R}$

Published on 28 Mar 2026 - 14:19

score 462 · Answer 9 · 2019-05-24 04:53:06

462

Views

Help understanding Polya's proof of the Arithmetic-Geometric Mean Inequality

Published on 24 May 2019 - 4:53

score 190 · Answer 10 · 2019-05-24 15:21:44

190

Views

Well ordering principle proof

Published on 24 May 2019 - 15:21

score 74 · Answer 11 · 2026-03-29 18:32:19

74

Views

Connection between fundamental group of circle and division by zero

Published on 29 Mar 2026 - 18:32

score 92 · Answer 12 · 2026-03-25 11:02:21

92

Views

understanding one step of Gödel's theorem

Published on 25 Mar 2026 - 11:02

score 41 · Answer 13 · 2019-05-24 20:29:54

41

Views

Every metric space is the union of open balls.

Published on 24 May 2019 - 20:29

score 1.9k · Answer 14 · 2026-03-26 20:25:48

1.9k

Views

Union of infinite sets and infinity

Published on 26 Mar 2026 - 20:25

score 159 · Answer 15 · 2026-03-26 09:49:21

159

Views

Proof that $a < b$ if and only if $a{+\!+} ≤ b$

Published on 26 Mar 2026 - 9:49

List Question

Prove by induction that, for all $n\in\Bbb N$, $\sqrt{n} ≤ \sum_ {k=1}^n \frac{1}{\sqrt{k}} < \sqrt{n} + \frac{n}{\sqrt{n+1}}$.

Deriving the information for Cramer-Rao Inequality

Hatcher's proof of proposition (c) for covering spaces

Can anyone elucidate vague hint towards the contradiction of $x^{-1}x=1$ and $x0=0$ in $x\in R/0$ $ \implies$ $x^{-1}\in R/0$ in an author's proof?

Symmetric Operators

Vector spaces are not rigid

Tricky proof of inequality

Suppose that the average value on all intervals $[a,b]$ is equal to $f((a+b)/2)$. Prove that $f''(x) = 0$ for all $x \in \mathbb{R}$

Help understanding Polya's proof of the Arithmetic-Geometric Mean Inequality

Well ordering principle proof

Connection between fundamental group of circle and division by zero

understanding one step of Gödel's theorem

Every metric space is the union of open balls.

Union of infinite sets and infinity

Proof that $a < b$ if and only if $a{+\!+} ≤ b$

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