My Math Forum Sequence of "stacked" square roots

 Calculus Calculus Math Forum

 March 26th, 2017, 03:59 PM #1 Senior Member     Joined: Nov 2015 From: United States of America Posts: 198 Thanks: 25 Math Focus: Calculus and Physics Sequence of "stacked" square roots Hello all. I am working on a sequence problem involving square roots. Here is my work: http://i.imgur.com/N3If5GR.jpg I need to figure out if it converges or diverges and then the value if it converges. I have been trying to figure out a formula for the denominator of the exponent so it matches the respected root in each term, but I can't figure it out. Is there another way to do this without trying to find a formula for the nth term? Thanks!
 March 26th, 2017, 04:36 PM #2 Senior Member   Joined: Aug 2012 Posts: 2,356 Thanks: 737 It seems pretty clear the sequence converges to 1. It's like repeatedly punching the square root button on your calculator. What is the 16-th root of 2? It's 1.000-something. It has to be bigger than 1 but not much bigger. Thanks from topsquark
 March 26th, 2017, 04:43 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra Look at the logarithm (base 2) of each element if Maschke's statement is either not obvious enough or not rigorous enough. Thanks from topsquark and SenatorArmstrong
March 26th, 2017, 05:40 PM   #4
Senior Member

Joined: Nov 2015
From: United States of America

Posts: 198
Thanks: 25

Math Focus: Calculus and Physics
Quote:
 Originally Posted by v8archie Look at the logarithm (base 2) of each element if Maschke's statement is either not obvious enough or not rigorous enough.
Hmm... Help me here. How do I relate log base 2 to roots here? I am missing the relationship here. Thanks for your response.

March 26th, 2017, 06:43 PM   #5
Math Team

Joined: May 2013
From: The Astral plane

Posts: 2,257
Thanks: 928

Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
 Originally Posted by SenatorArmstrong Hmm... Help me here. How do I relate log base 2 to roots here? I am missing the relationship here. Thanks for your response.
Take $\displaystyle log_2$ of each term in the series. For example
$\displaystyle 2^{1/3} \to log_2(~2^{1/3}) = 1/3$

Do that to each term. Does this give you any ideas?

-Dan

 March 26th, 2017, 06:44 PM #6 Senior Member     Joined: Nov 2015 From: United States of America Posts: 198 Thanks: 25 Math Focus: Calculus and Physics Got it now. Formula for the nth term is 2^[1/2^(n-1)] Taking the limit as n approaches infinity equals 1.

 Tags roots, sequence, square, stacked

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Sebastian Garth Number Theory 6 October 25th, 2013 07:21 PM Rumi Applied Math 3 October 11th, 2012 10:40 AM SedaKhold Calculus 0 February 13th, 2012 11:45 AM scherz0 Calculus 1 October 17th, 2009 04:38 AM katie0127 Advanced Statistics 0 December 3rd, 2008 01:54 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top