
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
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): $\displaystyle \sum_{i=1}^{\left< \frac{x+1}{2}\right>}\left< \log (\frac{x}{2i1})+1\right> = x$ So naturally I wanted to try (just without the floor): $\displaystyle \lim_{\infty} \frac{\sum_{i=1}^{\left< \frac{x+1}{2}\right>}\log (\frac{x}{2i1})+1}{x}$ 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  
Senior Member Joined: Dec 2012 Posts: 917 Thanks: 23  Quote:
 
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  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
function with limit  panky  Calculus  1  September 11th, 2016 05:15 AM 
Limit of function  HallsofIvy  Calculus  0  November 8th, 2012 07:52 AM 
Limit of the function  Vasily  Calculus  5  June 17th, 2012 02:25 PM 
limit of a function  martin_angelov  Calculus  3  June 10th, 2012 12:27 PM 
limit of a function  martin_angelov  Algebra  1  January 1st, 1970 12:00 AM 