# Sequence of real numbers | Proof of convergence

by kingwinner
Tags: convergence, numbers, proof, real, sequence
 P: 1,633 Since you seem to have spent quite some time on the problem i will try to give you some hints, i hope i don't get another warning from pf moderators for offering too much help(solving >90% of the problem for the op) :( This might not be the nicest proof in the world, but i think it works. As you have figured out the main problem is when 0a_0+a_1[/tex] If we continue in this fashion, after n-2 steps we would get something like: $$a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_n}>a_0+a_1+...+a_n>n*min\{a_0,a_1,...,a_ n\}=n*a$$ So, now you see that if we let n>N=1/a we get our result. where a=min{a_o,...,a_n} cheers!