I have to show that lim a_n = +(infinity) [as n->+(infinity)]
where a_1 >0
and:
a_(n+1) = a_n +(a_n)^(1/2) for all n>=1
It seems to me like it should be really easy, but for some reason I'm struggling.
I proved it is continues, strictly positive, and strictly increasing;
I figure the obvious thing to do is show that it is unbounded, and therefore since it is strictly increasing it diverges to +(infinity), but I'm really struggling to prove that it's unbounded.
Any help either proving it's unbounded above, or just divergent in general would be greatly appreciated!
2007-10-09
18:44:33
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3 answers
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asked by
greeneggs4spam
3
in
Mathematics