My Math Forum Limit with sequence

 Real Analysis Real Analysis Math Forum

 May 12th, 2019, 11:14 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 605 Thanks: 88 Limit with sequence Evaluate $\displaystyle \lim_{n\rightarrow \infty} \frac{(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n})^ n }{n}$. To write it in short-terms : $\displaystyle \lim_{n\rightarrow \infty}n^{-1}H_{n}^{n} \;$ , H is the harmonic series .
 May 13th, 2019, 01:03 PM #2 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 In general $\frac{x^n}{n}\to \infty$ for $x\gt 1$. Since the harmonic series diverges, the expression $\to \infty$. Thanks from idontknow

 Tags limit, sequence

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post idontknow Real Analysis 6 February 27th, 2019 03:48 AM henry12345 Real Analysis 5 July 17th, 2012 12:39 AM rubik2008 Calculus 3 July 2nd, 2012 06:56 PM nappysnake Calculus 2 December 11th, 2011 12:17 PM geyikrali Real Analysis 4 April 11th, 2008 12:29 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top