Finite and Infinite Sequences in Math

definition of sequence in math

Finite and Infinite Sequence in Math

1. Finite Sequence:

A sequence {sn} is said to be a finite sequence if the range of the sequence is finite.

Example 1:

The range of the sequence \left\{ {{{\left( { - 1} \right)}^n}} \right\} = \left\{ { - 1,1} \right\}, is a finite set, so this sequence is a finite sequence.

Example 2:

The range of the sequence \left\{ {a,a,a,a, \ldots } \right\} = \left\{ a \right\}, is a finite set, so this sequence is a finite sequence.

2. Infinite Sequence:

A sequence {sn} is said to be an infinite sequence if the range of the sequence is infinite.

Example 1:

The range of the sequence \left\{ {\frac{1}{{n + 1}}} \right\} = \left\{ {\frac{1}{{n + 1}},n \in N} \right\} = \left\{ {\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5}, \ldots } \right\}, is an infinite set, so this sequence is an infinite sequence.

Example 2:

The range of the sequence \left\{ {\frac{{{{\left( { - 1} \right)}^n}}}{n}} \right\} = \left\{ { - 1,\frac{1}{2}, - \frac{1}{3},\frac{1}{4}, - \frac{1}{5}, \ldots } \right\}, is an infinite set, so this sequence is an infinite sequence.

Note: We know that, the set of all distinct (different) terms of a sequence is called its range. We write all of the sequence’s elements in the range, but none of them is repeated. 


Finite and Infinite Sequences in Math in Hindi

1. परिमित अनुक्रम (Finite Sequence):

यदि अनुक्रम {sn} का परिसर (range) परिमित है, तो उस अनुक्रम को परिमित अनुक्रम कहते है।

उदाहरण 1:

अनुक्रम \left\{ {{{\left( { - 1} \right)}^n}} \right\} का परिसर \left\{ { - 1,1} \right\} है, जो एक परिमित समुच्चय है, इसलिए यह अनुक्रम एक परिमित अनुक्रम है।

उदाहरण 2:

अनुक्रम \left\{ {a,a,a,a, \ldots } \right\} का परिसर \left\{ a \right\} है, जो एक परिमित समुच्चय है, इसलिए यह अनुक्रम एक परिमित अनुक्रम है।

2. अपरिमित अनुक्रम (Infinite Sequence):

यदि अनुक्रम {sn} का परिसर (range) अपरिमित है, तो उस अनुक्रम को अपरिमित अनुक्रम कहते है।

उदाहरण 1:

अनुक्रम \left\{ {\frac{1}{{n + 1}}} \right\} का परिसर \left\{ {\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5}, \ldots } \right\} है, जो एक अपरिमित समुच्चय है, इसलिए यह अनुक्रम एक अपरिमित अनुक्रम है।

उदाहरण 2:

अनुक्रम \left\{ {\frac{{{{\left( { - 1} \right)}^n}}}{n}} \right\} का परिसर \left\{ { - 1,\frac{1}{2}, - \frac{1}{3},\frac{1}{4}, - \frac{1}{5}, \ldots } \right\} है, जो एक अपरिमित समुच्चय है, इसलिए यह अनुक्रम एक अपरिमित अनुक्रम है।

नोट: हम जानते हैं कि किसी अनुक्रम के सभी भिन्न (अलग-अलग) पदों के समुच्चय को उसका परिसर कहा जाता है। हम परिसर में अनुक्रम के सभी अवयवों को लिखते है , लेकिन उन अवयवों में से कोई भी अवयव दोहराया नहीं जाता है।



Copyrighted Material © 2019 - 2024 Prinsli.com - All rights reserved

All content on this website is copyrighted. It is prohibited to copy, publish or distribute the content and images of this website through any website, book, newspaper, software, videos, YouTube Channel or any other medium without written permission. You are not authorized to alter, obscure or remove any proprietary information, copyright or logo from this Website in any way. If any of these rules are violated, it will be strongly protested and legal action will be taken.



About Lata Agarwal 270 Articles
M.Phil in Mathematics, skilled in MS Office, MathType, Ti-83, Internet, etc., and Teaching with strong education professional. Passionate teacher and loves math. Worked as a Assistant Professor for BBA, BCA, BSC(CS & IT), BE, etc. Also, experienced SME (Mathematics) with a demonstrated history of working in the internet industry. Provide the well explained detailed solutions in step-by-step format for different branches of US mathematics textbooks.

Be the first to comment

Leave a Reply

Your email address will not be published.


*