My Math Forum Harmonic Series

 Real Analysis Real Analysis Math Forum

 December 8th, 2010, 12:01 PM #1 Senior Member   Joined: Apr 2009 Posts: 106 Thanks: 0 Harmonic Series 1/a + 1/(a+1) + 1/(a+2) + ... + 1/(a^2) > 1 Why does this prove that the harmonic series diverges to infinity? What is so important about the finite number of terms?
 December 8th, 2010, 12:14 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Harmonic Series 1 + 1/2 + 1/3 + 1/4 + ... = (1) + (1/2 + 1/3 + 1/4) + (1/5 + ...) + ... >= 1 + 1 + 1 + ...
 December 8th, 2010, 12:38 PM #3 Senior Member   Joined: Nov 2010 Posts: 502 Thanks: 0 Re: Harmonic Series The idea is that if you have an infinite number of finite sets, each of which add to a single number, then the total sum must diverge (assuming, of course, that the terms are all positive). Alternately, the harmonic series diverges and so it is not bounded by any number. Let's say we know that adding up the first k elements of the series gives us some number above the integer N. Then I know that adding the next (k+1)^2 elements will be above the integer N+1. In this fashion, one can see the series gets arbitrarily large.

 Tags harmonic, series

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Daltohn Calculus 3 March 2nd, 2014 12:31 PM lime Number Theory 4 June 29th, 2010 06:52 AM brunojo Real Analysis 11 December 2nd, 2007 07:49 AM astro_girl_690 Physics 5 January 13th, 2007 11:03 AM astro_girl_690 Algebra 3 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top