x(n) - x(n)*x(n-1) = x(n-1)
x(n-1)*(1 + x(n)) = x(n)
x(n-1) = x(n)/(1+x(n))
So
4 kill "initterm.txt"
5 open "initterm.txt" for output as #2
10 X=2015:Lvl=2015
20 for Lvl=2014 to 0 step -1
30 X=X//(1+X)
35 print #2,Lvl,X
40 next
45 close #2
50 print X
In the first few terms the numerator remains 2015, but the denominator, initially 1, goes up by 2015 each successively smaller subscript
n x(n)
2014 2015//2016
2013 2015//4031
2012 2015//6046
2011 2015//8061
2010 2015//10076
2009 2015//12091
2008 2015//14106
2007 2015//16121
2006 2015//18136
2005 2015//20151
...
and the last few are:
...
9 2015//4042091
8 2015//4044106
7 2015//4046121
6 2015//4048136
5 2015//4050151
4 2015//4052166
3 2015//4054181
2 2015//4056196
1 2015//4058211
0 2015//4060226
So x(0) = 2015/4060226
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Posted by Charlie
on 2015-07-21 15:08:06 |
electronically computed
