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   sci.math.symbolic      Symbolic algebra discussion      10,432 messages   

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   Message 9,912 of 10,432   
   j4n bur53 to bursejan@gmail.com   
   Re: lim n->oo problem solvable by CAS on   
   22 Jun 18 19:37:37   
   
   From: janburse@fastmail.fm   
      
   For a numerical exploration, I don't know whether   
   a Richard Fateman approach with BigFloat works.   
   I didn't try yet some BigFloat.   
      
   For some numerical exploration I did bignum   
   numerator and denumerator, and then computed   
   a simple float. But there was a surprise:   
      
   The fast Prolog system (faster in 9^(9^9)), gave   
   me the following result:   
      
       f(140)=0.6395241669738542   
       f(141)=0.6394713374128419   
       f(142)=0.6394192564631295   
       ERROR: Arithmetic: evaluation error: `float_overflow'   
      
   The slower Prolog system (slower in 9^(9^9)), didn't   
   stumble, gave me the following result:   
      
       f(140)=0.639524166973854   
       f(141)=0.639471337412842   
       f(142)=0.639419256463129   
       f(143)=0.639367908324447   
       f(144)=0.639317277638064   
       Etc..   
      
   Ha Ha   
      
   bursejan@gmail.com schrieb:   
   > Can a modern CAS solve this limit. I tried   
   > with Wolfram Alpha but with no avail:   
   >   
   >               n^1 + n^2 + ... + n^(n-1) + n^n   
   >    lim n->oo  ------------------------------- = ?   
   >               1^n + 2^n + ... + (n-1)^n + n^n   
   >   
   > Also can a CAS quickly draw an accurate   
   > graph of the function f(n), lets say with   
   >   
   > for n=0..1000?   
   >   
      
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