Skip to content Skip to navigation

Connexions

You are here: Home » Content » Convergencia de Secuencias

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice Digital Scholarship

    This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "Señales y Sistemas"

    Click the "Rice Digital Scholarship" link to see all content affiliated with them.

  • Featured Content display tagshide tags

    This module is included inLens: Connexions Featured Content
    By: ConnexionsAs a part of collection: "Señales y Sistemas"

    Comments:

    "Señales y Sistemas is a Spanish translation of Dr. Rich Baraniuk's collection Signals and Systems (col10064). The translation was coordinated by an an assistant electrical engineering professor […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Lens for Engineering

    This module is included inLens: Lens for Engineering
    By: Sidney Burrus

    Click the "Lens for Engineering" link to see all content selected in this lens.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Convergencia de Secuencias

Module by: Richard Baraniuk. E-mail the authorTranslated By: Fara Meza, Erika Jackson

Based on: Convergence of Sequences by Richard Baraniuk

Summary: Este módulo presentra una introducción a la convergencia y se enfocara en la secuencia, su comportamiento y sus aproximaciones al infinito.

¿Qué es una Secuencia?

Definition 1: secuencia
Una secuencia es una función gn gn definida en los enteros positivos 'nn'. También denotamos una secuencia por: gn | n =1∞ n 1 gn

Ejemplo

Una secuencia de números reales: gn=1n gn 1 n

Ejemplo

Una secuencia vector: gn=( sinn⁢π2 cosn⁢π2 ) gn n 2 n 2

Ejemplo

Una secuencia de una función: g n ⁢t={1  if  0≤t<1n0  otherwise   g n t 1 0 t 1 n 0

nota:

Una función puede ser pensada como un vector de dimensión infinito donde por cada valor de 'tt' tenemos una dimensión.

Convergencia de Secuencias Reales

Definition 2: límite
Una secuencia gn | n =1∞ n 1 gn converge a un límite g∈R g si para todo ε>0 ε 0 existe un entero N N tal que ∀ i ,i≥N:|gi−g|<ε i i N gi g ε Usualmente denotamos un límite escribiendo limit   i → ∞ gi=g i gi g ó g i →g g i g
La definición anterior significa que no importa que tan pequeño hagamos εε, excepto para un número finito de g i g i 's, todos los puntos de la secuencia estan dentro de una distancia εε de gg.

Ejemplo 1

Dada las siguiente secuencia de convergencia :

gn=1n gn 1 n (1)
Intuitivamente podemos asumir el siguiente límite: limit   n → ∞ gn=0 n gn 0 . Ahora provemos esto rigurosamente, digamos que dado el número real ε>0 ε 0 . Escojamos N=⌈1ε⌉ N 1 ε , donde ⌈x⌉ x denota el menor entero mayor que xx. Entonces para n≥N n N tenemos |gn−0|=1n≤1N<ε gn 0 1 n 1 N ε Donde, limit   n → ∞ gn=0 n gn 0

Ejemplo 2

Ahora veamos la siguiente secuencia no-convergente gn={1  if  n=par-1  if  n=impar gn 1 n par -1 n impar Esta secuencia oscila entre 1 y -1, asi que nunca converge.

Problemas

Para practicar, diga cuales de las siguientes secuencias convergen y de el limite si este existe.

  1. gn=n gn n
  2. gn={1n  if  n=par-1n  if  n=impar gn 1 n n par -1 n n impar
  3. gn={1n  if  n≠potencia de 101  otherwise   gn 1 n n potencia de 10 1
  4. gn={n  if  n<1051n  if  n≥105 gn n n 10 5 1 n n 10 5
  5. gn=sinπn gn n
  6. gn=in gn n

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks