Possible squeeze theorem limit question

[physicsjock]

http://img96.imageshack.us/img96/8606/qqqqbj.jpg

so what I'm thinking is that you let

x_n+3 + x_n+2<=x_n+2 + x_n+1 <= x_2 + x_1

then show that the first term can eventually go to the last term

squeezing the term into the middle

but the problem with this is i don't see where the 1/3 comes from

any ideas?

 

[AGNuke]

The third term is AM of its previous two terms.