Recent content by lokisapocalypse

  1. L

    Undergrad Solving a Diophantine Equation with $4000 and Cows, Lambs & Piglets

    Never mind. Amazing how after looking at this problem for 4 hours, I post it here and 20 minutes later I see my mistake.
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    Undergrad Solving a Diophantine Equation with $4000 and Cows, Lambs & Piglets

    The question reads: A farmer purchased 100 head of livestock for a total cost of $4000. Prices were as follow: calves, $120 each; lambs, $50 each; piglets, $25 each. If the farmer obtained at least one animal of each type, how many of each did he buy? I obtained that -240 < t < -15.789 but...
  3. L

    Proving Convergence of a Sequence with Upper Bound of 2

    Okay got it. Thanks for all your help.
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    Proving Convergence of a Sequence with Upper Bound of 2

    Okay I guess I am just stupid then. Where exactly do you type \sqrt{2 a_n} ? I thought it was to surround it by CODE tags but that didn't do it and I tried typing it just by itself, with and without the \. What do I do then?
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    Proving Convergence of a Sequence with Upper Bound of 2

    Oh nevermind about the limit part. It was proved in the book with the Monotone Convergence Theorem. I just didn't see it right away.
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    Proving Convergence of a Sequence with Upper Bound of 2

    Thanks I got it from that. But can someone tell me how to do the root thing? Is the code LaTeX code or what is it? Also, how can I prove the limit of that sequence = 2? Is there some theorem that says that the limit of an increasing bounded sequence is equal to the sup of that sequence?
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    Proving Convergence of a Sequence with Upper Bound of 2

    Hey guys, I have a sequence, \sqrt{2}, \sqrt{2 \sqrt{2}}, \sqrt{2 \sqrt{2 \sqrt{2}}}, ... Basically, the sequence is defined as x1 = root 2 x(n+1) = root (2 * xn). I need to show that this sequence converges and find the limit. I proved by induction that this sequence increases...
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    Graduate Proving Group Properties of \left< U_n, \cdot \right>

    And if all else fails for closure, you could list all the combinations of the elements and show that they each give you something back in Un. Although that would be the REALLY long way to go.
  9. L

    Undergrad Is the System of Equations Inconsistent Despite a Solved Example?

    It's amazing how simple a problem can be the 4th time around. If I had a dollar for every simple error like that I've made...
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    What Values of b Satisfy the Inequality 1296(b^3) - 324(b^2) - 1008b + 108 > 0?

    I have an inequality: 1296(b^3) - 324(b^2) - 1008b + 108 > 0. I want to know for what values of b this inequality is true. Any suggestions?
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    Proving the Algebraic Nature of Root 3 + Root 2 Using Polynomial Expressions"

    I apologize for the multiple post...I was in a panic. Won't happen again.
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    Proving the Algebraic Nature of Root 3 + Root 2 Using Polynomial Expressions"

    According to Maple, that gives -.30e-7.
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    Undergrad Proving Algebraic Nature of Root 3 + Root 2

    I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0...
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    Undergrad Proving an Algebraic Number: Root 3 + Root 2

    I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0...
  15. L

    Proving the Algebraic Nature of Root 3 + Root 2 Using Polynomial Expressions"

    I need to show that this is an algebraic number. In other words, I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 = where the a terms are not ALL 0 but some of them can be. Like for root 2 by itself, I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0