My Math Forum Convergence of sequence

 Calculus Calculus Math Forum

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
 20180904_214924.jpg (90.6 KB, 14 views)

 September 4th, 2018, 12:59 PM #2 Senior Member     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.
 September 4th, 2018, 01:21 PM #3 Global Moderator   Joined: Dec 2006 Posts: 19,887 Thanks: 1836 Or just $\displaystyle \text{QPochhammer}\small\left[ \frac 1 2\right]$.
 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.

 Tags convergence, divergence, limit, sequence

 Thread Tools Display Modes Linear Mode

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

 Contact - Home - Forums - Cryptocurrency Forum - Top