IMOSL-1990-7 (Modified)

Discussion on International Mathematical Olympiad (IMO)
User avatar
Phlembac Adib Hasan
Posts: 1016
Joined: Tue Nov 22, 2011 7:49 pm
Location: 127.0.0.1
Contact:

IMOSL-1990-7 (Modified)

Unread post by Phlembac Adib Hasan » Sun Feb 12, 2012 9:36 pm

Let $f(0)=f(1)=0$ and \[f(n+2)=4^{n+2}f(n+1)-16^{n+1}f(n)+n.2^{n^2},\; \; \; \; n\epsilon \mathbb{N}_0\]
Write $f(n)$ in terms of $n$.
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

User avatar
zadid xcalibured
Posts: 217
Joined: Thu Oct 27, 2011 11:04 am
Location: mymensingh

Re: IMOSL-1990-7 (Modified)

Unread post by zadid xcalibured » Sun Feb 12, 2012 10:16 pm

u modified nothing.just a part of the problem.this can be done defining another sequence in terms of f and then telescoping twice.

User avatar
Phlembac Adib Hasan
Posts: 1016
Joined: Tue Nov 22, 2011 7:49 pm
Location: 127.0.0.1
Contact:

Re: IMOSL-1990-7 (Modified)

Unread post by Phlembac Adib Hasan » Sun Feb 12, 2012 10:36 pm

zadid xcalibured wrote:u modified nothing.just a part of the problem.this can be done defining another sequence in terms of f and then telescoping twice.
Well, I didn't solve it in that way.I solved it by starting to find residues from $2$ to $1991$.That's why I said this "modified".
Welcome to BdMO Online Forum. Check out Forum Guides & Rules

User avatar
zadid xcalibured
Posts: 217
Joined: Thu Oct 27, 2011 11:04 am
Location: mymensingh

Re: IMOSL-1990-7 (Modified)

Unread post by zadid xcalibured » Sun Feb 12, 2012 10:45 pm

will u post ur solution?

Post Reply