My Math Forum how can solve this series?

 Real Analysis Real Analysis Math Forum

 January 30th, 2013, 01:43 PM #1 Newbie   Joined: Jan 2013 Posts: 13 Thanks: 0 how can solve this series? Hi all, I have to study the convergence of this series: $\sum \limits_{k=2}^\infty $$\frac {1}{ln(k)}- \frac {1}{ln(k+1)}$$$ I know (from wolfram) that for the comparison test the series converges (in particularly to 1,4427) I know that if I find a new series, b(k), such that for all k b(k)>a(k) then if b(k) converges also a(k) converges.. but what is b(k)? and what is the right method to find it? thanks to all, and I'm sorry for my bad english
 January 30th, 2013, 04:35 PM #2 Member     Joined: Mar 2011 Posts: 49 Thanks: 5 Re: how can solve this series? Hello! The partial sum for this serie is $S_n=\sum_{k=2}^n $$\frac{1}{\ln k} - \frac{1}{\ln(k+1)}$$$ by telscoping : $S_n=\frac{1}{\ln 2} - \frac{1}{\ln(n+1)} \)$ The sum of the serie is: $\lim_{n \to +\infty} S_n=\frac{1}{\ln 2}$

 Tags series, solve

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post g0bearmon Real Analysis 2 May 22nd, 2012 01:10 PM The_big_dill Algebra 5 June 1st, 2010 06:16 AM Crystal-Field Calculus 3 April 29th, 2009 07:12 PM mathmusic Calculus 1 March 19th, 2009 12:41 AM llinocoe Real Analysis 1 February 23rd, 2009 03:18 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top