Question

Prove sequence $x_n = \frac{3n+5}{\sqrt{4n^2 - 1}}$ is bounded.

score 562 · Answer 1 · 2026-04-16 23:18:38

562

Views

Prove sequence $x_n = \frac{3n+5}{\sqrt{4n^2 - 1}}$ is bounded.

Published on 16 Apr 2026 - 23:18

score 1.5k · Answer 2 · 2026-04-15 07:25:38

1.5k

Views

If f is a monotone function which defined on interval, then f is measurable

Published on 15 Apr 2026 - 7:25

score 735 · Answer 3 · 2026-04-16 11:47:23

735

Views

If $f$ is monotonic on $(a,b)$, the set of points of (a,b) at which $f$ is discontinuous is at most countable.

Published on 16 Apr 2026 - 11:47

score 44 · Answer 4 · 2026-04-14 22:29:43

44

Views

On the monotonicity of a certain sequence

Published on 14 Apr 2026 - 22:29

score 193 · Answer 5 · 2026-04-15 21:16:27

193

Views

Prove $x_n = \frac{n-3}{\sqrt{n^2+1}}$ is monotonic starting from some $n_0$.

Published on 15 Apr 2026 - 21:16

score 55 · Answer 6 · 2026-04-15 22:04:35

55

Views

Find relation between $a,b,c,d$ such that $\{x_n\} = \frac{an + b}{cn+d}$ is increasing/decreasing starting from some $n_0$.

Published on 15 Apr 2026 - 22:04

score 3.1k · Answer 7 · 2026-04-11 16:59:59

3.1k

Views

Verifying an increasing function on a closed interval is Riemann Integrable

Published on 11 Apr 2026 - 16:59

score 155 · Answer 8 · 2026-04-17 10:14:26

155

Views

Proof verification of if $\{x_n\}$ is monotone then $\{y_n\} = {1\over x_1 + x_2 + \dots + x_n}$ is monotone

Published on 17 Apr 2026 - 10:14

score 53 · Answer 9 · 2026-04-14 22:43:40

53

Views

Proof verification of $\{x_n\} = \left(1 + {1\over 2n}\right)^n$ is an increasing sequence.

Published on 14 Apr 2026 - 22:43

score 405 · Answer 10 · 2026-05-06 17:19:50

405

Views

Monotone Increasing Concave Function

Published on 06 May 2026 - 17:19

score 41 · Answer 11 · 2026-04-16 19:03:32

41

Views

Show that $x_n = \left(1+{x\over n}\right)^{n+k}$ is decreasing for $0<x<k$; $n, k\in \mathbb N$

Published on 16 Apr 2026 - 19:03

score 62 · Answer 12 · 2026-04-15 14:42:38

62

Views

Show that for $a \ne 1$, $a > 0$ the sequence $\{x_n\} = n(1-a^{1\over n})$ is increasing

Published on 15 Apr 2026 - 14:42

score 70 · Answer 13 · 2026-04-14 17:00:31

70

Views

Show that $x_{n+1} = \frac{x_n + 1}{n+1}$ is decreasing starting from some $n_0$ and find $n_0$.

Published on 14 Apr 2026 - 17:00

score 391 · Answer 14 · 2026-04-17 00:43:31

391

Views

Show $x_{n+1} = {1\over 2}x_n^2 - 1$ is bounded below and unbounded above and $x_n$ is increasing.

Published on 17 Apr 2026 - 0:43

score 67 · Answer 15 · 2026-04-10 22:38:53

67

Views

Proof that function is increasing

Published on 10 Apr 2026 - 22:38

List Question

Prove sequence $x_n = \frac{3n+5}{\sqrt{4n^2 - 1}}$ is bounded.

If f is a monotone function which defined on interval, then f is measurable

If $f$ is monotonic on $(a,b)$, the set of points of (a,b) at which $f$ is discontinuous is at most countable.

On the monotonicity of a certain sequence

Prove $x_n = \frac{n-3}{\sqrt{n^2+1}}$ is monotonic starting from some $n_0$.

Find relation between $a,b,c,d$ such that $\{x_n\} = \frac{an + b}{cn+d}$ is increasing/decreasing starting from some $n_0$.

Verifying an increasing function on a closed interval is Riemann Integrable

Proof verification of if $\{x_n\}$ is monotone then $\{y_n\} = {1\over x_1 + x_2 + \dots + x_n}$ is monotone

Proof verification of $\{x_n\} = \left(1 + {1\over 2n}\right)^n$ is an increasing sequence.

Monotone Increasing Concave Function

Show that $x_n = \left(1+{x\over n}\right)^{n+k}$ is decreasing for $0<x<k$; $n, k\in \mathbb N$

Show that for $a \ne 1$, $a > 0$ the sequence $\{x_n\} = n(1-a^{1\over n})$ is increasing

Show that $x_{n+1} = \frac{x_n + 1}{n+1}$ is decreasing starting from some $n_0$ and find $n_0$.

Show $x_{n+1} = {1\over 2}x_n^2 - 1$ is bounded below and unbounded above and $x_n$ is increasing.

Proof that function is increasing

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