All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math > Calculus
Floor Limit (Posted on 2014-05-26) Difficulty: 3 of 5
Let g(n) = n - [n/2] + [n/3] - [n/4] + ....

Evaluate this limit:
Limit g(n)/n
n → ∞
*** [x] is the greatest integer ≤ x

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution Comment 1 of 1
As n gets larger and larger,the effect of the floor function will become less and less as the dropped fractions will be divided by ever larger n (infinitely large in the "limiting" value of n).

The result, therefore will be the same as the ordinary alternating harmonic series, that is,the natural log of 2.

  Posted by Charlie on 2014-05-26 13:21:08
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2021 by Animus Pactum Consulting. All rights reserved. Privacy Information