Recent content by economist1985

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    Improper Integrals: Solving for Integrability of log^a(x)/x^p

    Homework Statement For what p is f(x)=log^a(x)/x^p integrable from (1,infinity)? Homework Equations The Attempt at a Solution I'm not sure, maybe I can do some sort of inequality so that I can arrive at the comparison theorem for improper integrals.
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    Show Limit Theorem: Sum of Sequence is L

    Sheesh, should have seen that. Thanks!
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    Show Limit Theorem: Sum of Sequence is L

    Homework Statement Suppose that a_n->L as n->infinity. Show that (a1+a2+...+an)/n=L as well. Homework Equations The Attempt at a Solution I'm thinking something about limit theorems here?
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    Convergence for recursive sequence

    Homework Statement Let x_1=1 and let x_n=x_n-1 + 1/n^n for n>1. Show that x1, x2, ... is convergent. Homework Equations The Attempt at a Solution I have managed to transform x_n=summation(1/n^n). How do I show that this is convergent?
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    Simple analysis continuity problem

    Oh I think I got it. Thanks
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    Simple analysis continuity problem

    Thanks for the explanation. The problem is clearer now to me. What I still do not get is how the epsilon delta definition guarantees it. ?? Sorry if I can't follow through... I'm new to this.
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    Simple analysis continuity problem

    Homework Statement If f is a real function which is continuous at a element R and if f(a)<M for some M element of R, prove that there is an open interval I containing a such that f(x)<M for all x element of I. Homework Equations Extreme value theorem, intermediate value theorem...
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    Simple analysis proof: x^n -> a^n as x -> a

    still, how do you show that (x^(n-1)+x^(n-2)*a+ ... + a^(n-1)) is < epsilon?