Solved

mathematic problem

Posted on 2013-05-15
3
401 Views
1 Endorsement
Last Modified: 2013-05-15
How to prove that for n > 2  
n to degree of n+1 is larger than (n+1) to degree of n
1
Comment
Question by:user_n
  • 2
3 Comments
 
LVL 32

Accepted Solution

by:
phoffric earned 500 total points
ID: 39167793
If n^(n+1) > (n+1)^n
then by dividing RHS ==>
n^(n+1) / (n+1)^n > 1 ==>
n * n^n / (n+1)^n > 1 ==>
n * [ n/(n+1)]^n > 1 ==>
n * [1/(1+1/n)]^n  > 1 ==>
n / (1 + 1/n)^n > 1
and for n > 2, then (1+1/n) < 2
so it is true that n / (1 + 1/n)^n > 1

Working backwards with this last fact, you find that n^(n+1) > (n+1)^n
0
 
LVL 9

Author Comment

by:user_n
ID: 39167836
Thank you very much
0
 
LVL 32

Expert Comment

by:phoffric
ID: 39167892
You're welcome
0

Featured Post

Is Your Active Directory as Secure as You Think?

More than 75% of all records are compromised because of the loss or theft of a privileged credential. Experts have been exploring Active Directory infrastructure to identify key threats and establish best practices for keeping data safe. Attend this month’s webinar to learn more.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Introduction On a scale of 1 to 10, how would you rate our Product? Many of us have answered that question time and time again. But only a few of us have had the pleasure of receiving a stack of the filled out surveys and being asked to do somethi…
Do you hate spam? I do, and I am willing to bet you do as well. I often wonder, though, "if people hate spam so much, why do they still post their email addresses on the web?" I'm not talking about a plain-text posting here. I am referring to the fa…
Learn how to match and substitute tagged data using PHP regular expressions. Demonstrated on Windows 7, but also applies to other operating systems. Demonstrated technique applies to PHP (all versions) and Firefox, but very similar techniques will w…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.

943 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

10 Experts available now in Live!

Get 1:1 Help Now