My Math Forum What is the limit of this function?

 Number Theory Number Theory Math Forum

 March 15th, 2017, 07:56 AM #1 Newbie   Joined: Mar 2017 From: Peru Posts: 2 Thanks: 0 What is the limit of this function? Hello, I was playing around with some sums and noticed that (the weird brackets are supposed to be the floor function and all logs are in base two): $\displaystyle \sum_{i=1}^{\left< \frac{x+1}{2}\right>}\left< \log (\frac{x}{2i-1})+1\right> = x$ So naturally I wanted to try (just without the floor): $\displaystyle \lim_{\infty} \frac{\sum_{i=1}^{\left< \frac{x+1}{2}\right>}\log (\frac{x}{2i-1})+1}{x}$ For x = 10000 it equals 1.221347 and it seems it converges around that value. Anyone know where does that value come from or how can I calculate it?
March 15th, 2017, 09:29 AM   #2
Banned Camp

Joined: Dec 2012

Posts: 1,028
Thanks: 24

Quote:
 Originally Posted by Ryunaq Hello, I was playing around with some sums and noticed that (the weird brackets are supposed to be the floor function and all logs are in base two): $\displaystyle \sum_{i=1}^{\left< \frac{x+1}{2}\right>}\left< \log (\frac{x}{2i-1})+1\right> = x$ So naturally I wanted to try (just without the floor): $\displaystyle \lim_{\infty} \frac{\sum_{i=1}^{\left< \frac{x+1}{2}\right>}\log (\frac{x}{2i-1})+1}{x}$ For x = 10000 it equals 1.221347 and it seems it converges around that value. Anyone know where does that value come from or how can I calculate it?
Is it $x=a ; a\in \mathbb{N^+}$ or else ?

 March 15th, 2017, 09:58 AM #3 Newbie   Joined: Mar 2017 From: Peru Posts: 2 Thanks: 0 Oh right, I forgot, It's only for positive natural numbers.

 Tags function, limit

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post panky Calculus 1 September 11th, 2016 05:15 AM HallsofIvy Calculus 0 November 8th, 2012 06:52 AM Vasily Calculus 5 June 17th, 2012 02:25 PM martin_angelov Calculus 3 June 10th, 2012 12:27 PM martin_angelov Algebra 1 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top