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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: 951 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.


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