
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 28th, 2017, 12:48 AM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 385 Thanks: 27 Math Focus: Number theory  Series sums' terms choice
Consider: Sum=11+11+11+11...=undefined; Or does Sum=(11)+(11)+(11)+(11)...=0 Please give me other simple examples for infinite summation series where choosing the gathering of terms seems to change its ambiguous outcome. 
March 28th, 2017, 11:35 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,126 Thanks: 1104 
nothing mysterious about this an infinite summation converges to a value only if the underlying sequence converges to 0 your underlying sequence here doesn't converge to 0 so anything you might have to say about it's infinite summation is meaningless 
March 28th, 2017, 01:32 PM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 385 Thanks: 27 Math Focus: Number theory  https://en.wikipedia.org/wiki/Grandi's_series Above is a great link I just found about such "naive" series summations. 
March 28th, 2017, 02:07 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond  
March 28th, 2017, 02:09 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,462 Thanks: 2499 Math Focus: Mainly analysis and algebra  This is the "orthodox" view which relies on us defining the sum to be undefined. Modern research is considerably less definite on the subject. There are good reasons to believe that $\frac12$ is a meaningful value of the series.


Tags 
choice, series, sums, terms 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Using series manipulations to find the sums of finite series  stevewilliams  Algebra  1  April 22nd, 2016 01:40 PM 
How to convert a series of sums to a function  extreme112  Calculus  3  February 1st, 2015 05:28 PM 
what are the sum of the first 8 terms of these series?  1love  Algebra  8  May 20th, 2012 08:49 PM 
Infinite series  finding sums  xdeathcorex  Calculus  4  August 31st, 2010 11:03 AM 
Series involving natural log and sums close to zero  peka0027  Real Analysis  3  April 2nd, 2009 05:22 AM 