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1d
revised What are the theorems in mathematics which can be proved using completely different ideas?
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1d
answered Integer solutions to $\frac{1}{a} + \frac{1}{b} = \frac{1}{12}$.
1d
comment Integer solutions to $\frac{1}{a} + \frac{1}{b} = \frac{1}{12}$.
It's \frac, not /frac.
1d
answered What are the theorems in mathematics which can be proved using completely different ideas?
1d
comment Proving that $1\cdot3+3\cdot5+5\cdot7+\cdots+(2n-1)(2n+1)={n(4n^2+6n-1) \over 3}$ by induction for $n\geq 1$
This description of Step 2, "When a statement is true for a natural number $n=k$, then it will also be true for its successor, $n=k+1$" is not correct. You have to start with the statement from Step 1 and deduce, using regular algebra steps, that a similar statement is true where each "$k$" has been replaced with "$(k+1)$". Your description sounds like you want to just swap out the "$k$" for the "$(k+1)$" right away.
1d
comment Is this:$\sum_{n=1}^{\infty}{(-1)}^{\frac{n(n-1)}{2}}\frac{1}{n}$ a convergent series?
@lulu Here the terms being grouped individually tend to $0$. This whole argument shows that there is a subsequence of the partial sums that converges. Any term of the general sequence of partial sums is within three terms of this convergent subsequence, and those three terms get arbitrarily small. The same kind of logic goes into the altenating series test.
2d
answered Proving that $1\cdot3+3\cdot5+5\cdot7+\cdots+(2n-1)(2n+1)={n(4n^2+6n-1) \over 3}$ by induction for $n\geq 1$
2d
comment Factorisation over $\Bbb C$ of $z^2 -10z+30$
If you multiply out the factors you have, you get a constant term of $20$. You need $-5$ under your two radicals. Or, as you say, introduce $i$ as coefficients to those radicals.
Jul
15
comment What is the most efficient numerical base system?
@ShreevatsaR Wouldn't "three" be $2.21211\ldots=2e^0+2e^{-1}+e^{-2}+2e^{-3}+e^{-4}+e^{-5}+\cdots$? It looks like you skipped over the ones place, and are actually expanding $10.0200112\ldots$, which would be an alternative.
Jul
11
comment Is it possible to find indefinite integral of $\int \frac{1} {{\sin(x)+\sec^2(x)}}\mathrm{d}x$?
A minor shortcut would come from not using the Weierstrass substitution, but rather rewriting the integrand in $\sin$ and $\cos$ as $\frac{\cos^2(x)}{\sin(x)\cos^2(x)+1}=\frac{\cos(x)\cdot\cos(x)}{\sin(x)(1-{\sin‌​^2} (x))+1}$ and substituting $u=\sin(x)$. Still leads to the same kind of thing as in (2) of course.
Jul
11
revised Find all constants where a matrix is symmetric
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Jul
11
comment Find all constants where a matrix is symmetric
The coeffiicient of $c$ in your first equation does not match what is in the matrix. Which one is the typo?
Jul
11
comment Find all constants where a matrix is symmetric
Math questions are often worded that way so as to not give away any extra information. It's up to you to establish there is exactly one solution, instead of zero, or more than one.
Jul
11
comment Find all constants where a matrix is symmetric
Is this system indeed correct? OP's 1,2 position has $a-2b+2c$, but the first equation OP wrote (and that this answer uses) has $a-2b+c$.
Jul
11
answered Find all constants where a matrix is symmetric
Jul
10
comment $R^2\setminus K, K$ compact, is not simply connected
Use \setminus for the \ (I think) you want to make.
Jul
9
comment “Negative” versus “Minus”
@chharvey "negative s" is "the negative of s", which in that example is "the negative of negative 8". To me with my background, "negative" already means "the opposite of", so it's a matter of background/culture/experience. (Also by the way, maybe "the opposite of 8" means "1/8", so there's no magic bullet.) But anyway, I think my comment (from three years ago!) was in response to GEdgar. I'm only making the point that the word "negative" is no better than the word "minus" when it comes to the potential for confusion here.
Jul
9
comment If x and y are real, solve the equation $\frac{xi}{1+yi}=\frac{3x+4i}{x+3y}$
Another approach: conjugate both sides of this equation to get a new equation. Now you have two equations in two variables.
Jul
8
revised Is Tolkien's Middle Earth flat?
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Jul
8
revised Is Tolkien's Middle Earth flat?
added 83 characters in body