http://www.learningcurve.gov.uk/

-

QUESTION;


Which is larger? 1999^1999 or 2000^1998

I am stumped.


-

ANSWER;

Let's look at some smaller versions of the same problem:

 n      n^n     (n+1)^(n-1)
 -     -----    -----------
 2         4              3
 3        27             16
 4       256            125
 5      3125           1296
 6     46656          16807

This is hardly a proof, but it suggests that the term with the
higher exponent will be larger.  If you can prove (e.g., by
induction) that n^n grows faster than (n+1)^(n-1), then it's got
to hold for the special case of n=1999.


!!
-

vector calculator Softw.


http://www.greuer.de/ecalc3d.html

-







-

Pi ......



http://en.wikipedia.org/wiki/Pi