
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
April 4th, 2018, 09:21 AM  #1 
Newbie Joined: Apr 2018 From: India Posts: 4 Thanks: 0  Infinite convergent series.
How do I find the limiting value of any convergent series ? I mean, how do I approach it? ("steps", maybe?) ex : (1^2)+(2^2)+(3^2)+.... = pi^2/6 I know the solution of this problem but how on earth did anyone (Euler) come up with this ? . . . . . ( I'm trying to solve this (1^3)+(2^3)+(3^3)+..... = ? ) 
April 4th, 2018, 09:30 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,501 Thanks: 1372  How Euler found the sum of inverse squares I don't believe there is a general strategy to your problem. You can try to match up the coefficients with a Taylor series. A handful of series, such as the geometric series, have known results. 
April 4th, 2018, 09:45 AM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra  
April 4th, 2018, 12:40 PM  #4 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,226 Thanks: 908 Math Focus: Wibbly wobbly timeywimey stuff. 
That was awesome. Thanks to romsek and v8archie for posting them. Dan 
April 4th, 2018, 02:35 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,671 Thanks: 2651 Math Focus: Mainly analysis and algebra 
Just remembered this mildly awesome one too, although it has less to do with Euler. 

Tags 
convergent, infinite, series 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Convergent series : cos(k^2)/k  Dattier  Real Analysis  14  June 27th, 2017 05:55 AM 
Convergent Series  Dmath  Calculus  2  June 4th, 2014 06:22 AM 
Estimate the Sum of A Convergent Series  xinglongdada  Calculus  1  June 26th, 2012 06:02 PM 
Is this series convergent?  nappysnake  Real Analysis  1  December 18th, 2011 06:49 PM 
Convergent series > series of geometric means converges  The Chaz  Real Analysis  11  February 7th, 2011 04:52 AM 