Question

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

score 559 · Answer 1 · 2018-10-23 16:26:55

559

Views

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

Published on 23 Oct 2018 - 16:26

score 1.5k · Answer 2 · 2018-10-26 05:22:32

1.5k

Views

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

Published on 26 Oct 2018 - 5:22

score 733 · Answer 3 · 2018-11-02 03:04:35

733

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 02 Nov 2018 - 3:04

score 41 · Answer 4 · 2018-11-02 14:45:51

41

Views

On the monotonicity of a certain sequence

Published on 02 Nov 2018 - 14:45

score 190 · Answer 5 · 2018-11-05 18:37:53

190

Views

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

Published on 05 Nov 2018 - 18:37

score 52 · Answer 6 · 2018-11-06 15:07:20

52

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 06 Nov 2018 - 15:07

score 3.1k · Answer 7 · 2018-11-07 23:04:11

3.1k

Views

Verifying an increasing function on a closed interval is Riemann Integrable

Published on 07 Nov 2018 - 23:04

score 152 · Answer 8 · 2018-11-08 12:56:16

152

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 08 Nov 2018 - 12:56

score 50 · Answer 9 · 2018-11-08 18:09:50

50

Views

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

Published on 08 Nov 2018 - 18:09

score 398 · Answer 10 · 2026-03-22 10:30:30

398

Views

Monotone Increasing Concave Function

Published on 22 Mar 2026 - 10:30

score 38 · Answer 11 · 2018-11-09 18:19:04

38

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 09 Nov 2018 - 18:19

score 60 · Answer 12 · 2018-11-10 13:37:00

60

Views

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

Published on 10 Nov 2018 - 13:37

score 67 · Answer 13 · 2018-11-13 16:32:33

67

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 13 Nov 2018 - 16:32

score 388 · Answer 14 · 2018-11-13 18:17:41

388

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 13 Nov 2018 - 18:17

score 64 · Answer 15 · 2018-11-14 10:29:41

64

Views

Proof that function is increasing

Published on 14 Nov 2018 - 10:29

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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