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| bio | website | |
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| age | ||
| visits | member for | 2 years, 3 months |
| seen | 12 hours ago | |
| stats | profile views | 1,194 |
I am not here with any regularity.
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1d |
comment |
Find the limit $ \lim_{n \to \infty}\left(\frac{a^{1/n}+b^{1/n}+c^{1/n}}{3}\right)^n$ I have edited your answer as it was quite startling to see such huge fonts. If you want to see the $\TeX$ I used, you can right click on the math and select "Show Math As -> TeX Commands" |
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1d |
revised |
Find the limit $ \lim_{n \to \infty}\left(\frac{a^{1/n}+b^{1/n}+c^{1/n}}{3}\right)^n$ deleted huge and large fonts, aligned equations, change e^x wiith exp(x), changed log to \log |
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1d |
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Number Theory $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd Even easier: $a \in \{1,3,5,7\} \implies a^2 \equiv 1 \pmod{8}$. |
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May 18 |
revised |
Proof using trigonometry that circle circumference is $2 \pi R$ fixed typos |
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May 18 |
comment |
Proof using trigonometry that circle circumference is $2 \pi R$ I should also mention that Michael Hardy mentioned that the circumference of a circle and its length are often confused, and I admit that I use the two terms interchangeably here. What I give up in precision, I make up for in getting my point across. |
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May 18 |
answered | Proof using trigonometry that circle circumference is $2 \pi R$ |
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May 18 |
comment |
Proving an inequality: $|1-e^{i\theta}|\le|\theta|$ +1: IIRC, the OP's problem appears in "Berkeley Problems in Mathematics" and your hint appears as their solution. |
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May 18 |
comment |
A binary quadratic form: $nx^2-y^2=2$ Related. |
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May 17 |
awarded | Constituent |
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May 17 |
comment |
Proof using trigonometry that circle circumference is $2 \pi R$ What is $\pi$ if not the ratio of a circle's circumference to the length of its diameter? |
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May 17 |
comment |
Proof f(x) is continuous given $x$ rational and irrational. Hint: Show that if $a \neq \frac{1}{2}$, then $\displaystyle \lim_{x \to a} f(x)$ does not exist. |
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May 17 |
comment |
Proof using trigonometry that circle circumference is $2 \pi R$ How do you define $\pi$? |
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May 17 |
comment |
Using the hypothesis $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{a+b+c}$ to prove something else +1, though I would add the words "Without loss of generality" before $a = -b$. The reason is that it may well not be the case that $a = -b$, but we know at least one of $a = -b, b = -c$, or $a = -c$ occurs, and all cases are dealt with similarly. |
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May 16 |
comment |
How to prove that $1/n!$ is less than $1/n^2$? Correction: the induction works for $n \geq 4$ as $3^2 \not< 3!$. |
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May 16 |
reviewed | Approve suggested edit on Test of convergence of $\int_{-\infty}^{\infty} \dfrac{x^6+6}{x^8+8}dx$ |
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May 16 |
answered | Legendre symbol proof |
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May 16 |
revised |
Solving systems of equations using matrices added 589 characters in body |
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May 16 |
comment |
Solving systems of equations using matrices I'm not sure I understand what you mean. Gauss-Jordan gives you a method for reducing all augmented matrices regardless of how messy the matrix. In other words, if you always follow the steps of Gauss-Jordan, you will eventually arrive at a matrix which is in reduced row echelon form. |
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May 16 |
comment |
Piecewise defined integration $f_n(x) = \frac{n}{2} \cdot 1_{\left[ - \frac{1}{n}, \frac{1}{n} \right]}(x)$, where $1_A(x)$ is the indicator function. |
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May 16 |
answered | Solving systems of equations using matrices |
