(In reply to my second answer
it only proves that series cannot be unambiguously defined by a finite, albeit large, quantity of samples...
e.g. 1,2,3,4,5,6,7 ,,,, a(n)=n will go on as 8,9,10,..etc
but a(n) =(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*(n-7)+n
produces 1,2,3,4,5,6,7,5048 ,9!+9,...
need I say more???