My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 4th, 2018, 12:50 PM   #1
Newbie
 
Joined: Mar 2018
From: Split, Croatia

Posts: 13
Thanks: 0

Convergence of sequence

Is this sequence convergent?
I rewrited this product so it looks simpler, so, in this fraction, I see the pattern by which the factors behave (the n-th factor in the numerator is the n-th factor in the denominator -1), but I don't have idea how to calculate that value, and determine if this sequence converges? Any help appreciated!
Attached Images
File Type: jpg 20180904_214924.jpg (90.6 KB, 14 views)
Birgitta is offline  
 
September 4th, 2018, 12:59 PM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,174
Thanks: 1143

Mathematica is calling the limit as $n \to \infty ~~\text{QPochhammer}\left[ \dfrac 1 2, \dfrac 1 2\right]$

It has a numeric value of approximately $0.2887881$.

Last edited by skipjack; September 4th, 2018 at 01:03 PM.
romsek is offline  
September 4th, 2018, 01:21 PM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 19,887
Thanks: 1836

Or just $\displaystyle \text{QPochhammer}\small\left[ \frac 1 2\right]$.
skipjack is offline  
September 10th, 2018, 10:54 PM   #4
Math Team
 
Joined: Nov 2014
From: Australia

Posts: 689
Thanks: 244

If you only want to know whether it converges, prove that it is decreasing and bounded below by 0. Then use the monotone convergence theorem.
Azzajazz is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
convergence, divergence, limit, sequence



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
sequence convergence dthiaw Pre-Calculus 4 June 1st, 2017 09:40 PM
Sequence convergence (Leibniz and absolute convergence) Chemist@ Calculus 7 November 1st, 2014 03:16 PM
Convergence of sequence elimax Real Analysis 3 July 1st, 2011 10:21 AM
sequence, convergence genoatopologist Real Analysis 2 February 25th, 2009 01:33 PM
sequence, convergence fermatprime371 Real Analysis 1 January 30th, 2009 10:13 AM





Copyright © 2018 My Math Forum. All rights reserved.