hello,
i have the function f(n) = [f(n-1)*(n-1+r)]/n, where f(1)=a
how can i solve this? does it converge or diverge? im not quite sure how i can go about this. The answer on wolfram alpha seems too complicated
#Solution of recurrent fucntion
feral ice
neon wolfBOT
fair dawn
Have you tried writing out the first dozen terms or so? If it's too complicated, try doing it for a specific value of r.
feral ice
Have you tried writing out the first dozen terms or so? If it's too complicated,...
yeah, visually i can see that it is probably:
f(n) = a *(n-1+r)! / (n!r!)
but even then im not sure how to continue from there.
do i just say n-> oo, so f(n) ->a/r! ?
fair dawn
(n-1+r)/n does got to 0 as n->infinity, but the same is not true of their factorials
consider (n+1)!/n! = n+1
so as n-> infinity, that fraction goes to infinity
feral ice
consider (n+1)!/n! = n+1
that doesnt appear anywhere tho, hmm
fair dawn
yeah, visually i can see that it is probably:
`f(n) = a *(n-1+r)! / (n!r!)`
but ...
it's what you wrote
feral ice
it's what you wrote
it is n-1+r tho, not n+1 :/
fair dawn
okay, so what if r=2?
feral ice
oh wait i read it wrong.
ok so what happens to their factorials as n->oo?
the whole thing diverges?
feral ice
is r allowed to equal 0?
no, it is part of an algorithm and the algorithm doesnt even really do anything useful if 0<r<1
what can you say about (n+x)!/n!, where x isnt an integer? does it have a closed form?