Saturday, 20 July 2013

algebra precalculus - Sum of irrational numbers

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Well, in this question it is said that $\sqrt[100]{\sqrt3 + \sqrt2} + \sqrt[100]{\sqrt3 - \sqrt2}$, and the owner asks for "alternativ...
Friday, 19 July 2013

Complex Numbers - Find the proof for "z"

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Hi I have a question on complex numbers, where I'm not sure how to go about dealing with it. This is what I need to do: Let $z=a+ib$, be...

polynomials - sum of square root of primes 2

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I dont know how to solve the problem below. (1) $p[1]$, $p[2]$, $\ldots$, $p[n]$ are distinct primes, where $n = 1,2,\ldots$ Let $a[n]$ be t...

calculus - Definition of an Infinitesimal

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Covering 1.4 of Keisler's Elementary Calculus, "Slope and Velocity; The Hyperreal Line" That chapter defines: A number $\epsil...

calculus - if $int_1^{infty}f(x) mathrm dx$ converges, must $int_1^{infty}f(x)sin x mathrm dx$ converge?

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I can't use any of the convergence tests I learned because I have no information on $f(x)$, in particular I don't know if it's c...

limits - How to compute $lim_{nrightarrowinfty}e^{-n}left(1+n+frac{n^2}{2!}cdots+frac{n^n}{n!}right)$

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There is a probabilistic method to solve it. But I am not familiar with probability. I am trying to compute it by analytic method, such as u...

induction - Prove that $a^{2n} -b^{2n}$ is divisible by $a+b$

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Prove that for all $n\in\Bbb{Z}$ , $a^{2n}-b^{2n}$ is divisible by $a+b$ using induction. I know that if $a$ is divisible by $b...