Facebook Page
Twitter
RSS
+ Reply to Thread
Results 1 to 7 of 7
  1. MHB Journeyman
    MHB Site Helper
    lfdahl's Avatar
    Status
    Offline
    Join Date
    Nov 2013
    Location
    Aabenraa, Denmark
    Posts
    716
    Thanks
    2,349 times
    Thanked
    1,454 time
    Thank/Post
    2.031
    Awards
    MHB Challenges Award (2017)  

Secondary School/High School POTW (2014)
    #1
    Show, that the identity

    \[\int_{0}^{1}\frac{x^{n-1}+x^{n-\frac{1}{2}}-2x^{2n-1}}{1-x}dx = 2\ln2\]

    - holds for any natural number $n$.

  2. # ADS
    Circuit advertisement
    Join Date
    Always
    Location
    Advertising world
    Posts
    Many
     

  3. MHB Journeyman
    MHB Site Helper
    lfdahl's Avatar
    Status
    Offline
    Join Date
    Nov 2013
    Location
    Aabenraa, Denmark
    Posts
    716
    Thanks
    2,349 times
    Thanked
    1,454 time
    Thank/Post
    2.031
    Awards
    MHB Challenges Award (2017)  

Secondary School/High School POTW (2014)
    #2 Thread Author

  4. MHB Apprentice
    Theia's Avatar
    Status
    Offline
    Join Date
    Mar 2016
    Posts
    81
    Thanks
    185 times
    Thanked
    179 times
    #3
    I'm sorry about poking a bit older threat, but I found this interesting, so here is my attempt:


  5. MHB Journeyman
    MHB Site Helper
    lfdahl's Avatar
    Status
    Offline
    Join Date
    Nov 2013
    Location
    Aabenraa, Denmark
    Posts
    716
    Thanks
    2,349 times
    Thanked
    1,454 time
    Thank/Post
    2.031
    Awards
    MHB Challenges Award (2017)  

Secondary School/High School POTW (2014)
    #4 Thread Author
    Thankyou, Theia, for a clever solution!

  6. MHB Master
    MHB Math Helper
    topsquark's Avatar
    Status
    Offline
    Join Date
    Aug 2012
    Location
    The Astral plane
    Posts
    1,061
    Thanks
    5,224 times
    Thanked
    1,922 time
    Thank/Post
    1.811
    Awards
    MHB Humor Award (2016)  

MHB Humor Award (2015)  

MHB Humor Award (2014)
    #5
    Quote Originally Posted by Theia View Post
    I'm sorry about poking a bit older threat, but I found this interesting, so here is my attempt:

    Interesting. I note that Theia's solution uses a derivative of n, which implies that n doesn't have to be natural number! (I double-checked this on W|A.)

    -Dan

  7. MHB Apprentice
    Theia's Avatar
    Status
    Offline
    Join Date
    Mar 2016
    Posts
    81
    Thanks
    185 times
    Thanked
    179 times
    #6
    Yes, $ \displaystyle n \in \mathbb{N}$ is not a crucial requirement for $ \displaystyle F'(n) = 0$. But I haven't yet found a proof that shows what is required for $ \displaystyle n$.

  8. MHB Apprentice
    MountEvariste's Avatar
    Status
    Offline
    Join Date
    Jun 2017
    Posts
    66
    Thanks
    194 times
    Thanked
    135 times
    #7
    Quote Originally Posted by Theia View Post
    I'm sorry about poking a bit older threat, but I found this interesting, so here is my attempt:

    It really is an interesting question.

    I've been thinking about it this evening, and wonder if what's below makes sense.

Similar Threads

  1. Definite Integral Challenge
    By anemone in forum Challenge Questions and Puzzles
    Replies: 2
    Last Post: May 7th, 2014, 08:51
  2. Definite Integral challenge #3
    By Pranav in forum Challenge Questions and Puzzles
    Replies: 8
    Last Post: March 17th, 2014, 01:04
  3. Definite Integral challenge #2
    By Pranav in forum Challenge Questions and Puzzles
    Replies: 2
    Last Post: February 25th, 2014, 04:43
  4. Definite integral challenge
    By MarkFL in forum Challenge Questions and Puzzles
    Replies: 5
    Last Post: December 15th, 2013, 17:01
  5. Definite integral challenge...
    By DreamWeaver in forum Challenge Questions and Puzzles
    Replies: 1
    Last Post: September 30th, 2013, 18:23

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Math Help Boards