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Alternating Series Test Proof
I am somewhat stuck on this proof of the alternating series test, could you please point me to the right direction ? Let $(a_n)$ be a decreasing sequence ...
Apr 20, 2026
Archive: News
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Why does the surface area of the hypersphere go to zero as the number of dimensions goes to infinity?
Why does the surface area of the hypersphere go to zero as the number of dimensions goes to infinity? Is there an intuitive reason?
Apr 19, 2026
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Find the equation of the parabola in which the ends of the latus rectum
Find the equation of the parabola in which the ends of the latus rectum have the coordinates $(-1,5)$ and $(-1,-11)$ and the vertex is $(-5,-3)$. I could ...
Apr 19, 2026
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Relationship between Diagonally dominant and Well Conditioned matrices
While solving linear systems by iterative methods is common pay attention to Diagonally dominant matrices, equivalently when studying stability of interpo...
Apr 19, 2026
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cubic function of the two points (2,0) (4,0)
How can I find the cubic function of two points. I have the $y$-intersect $(0,2)$ and the $y=0$ intersect with the x-axis $(4,0)$. The equation should hav...
Apr 19, 2026
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how $1/0.5$ is equal to $2$?
My question is how $1/0.5$ is equal to $2$. I am not asking the mathematical justification that $1/0.5=10/5=2$. I know all this. I just want to know how i...
Apr 19, 2026
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Twin, cousin, sexy, ... primes
Twin, cousin, and sexy primes are of the forms $(p,p+2)$, $(p,p+4)$, $(p,p+6)$ respectively, for $p$ a prime. The Wikipedia article on cousin primes says ...
Apr 19, 2026
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On the slope of a strictly increasing function
If $f$ is a strictly increasing function, shouldn't $f'$ be always positive and never zero? Apparently there's this situation where the der...
Apr 19, 2026
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How to calculate the number of possible license plate using the formula for combinations with repetitions allowed?
I'm having a little trouble reconciling two different methods for calculating the number of license plates that can be formed from three letters (fro...
Apr 19, 2026
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Factorising quadratics - coefficient of $x^2$ is greater than $1$
In factoring quadratics where the coefficient of $x^2$ is greater than $1$, I use the grouping method where we multiply the coefficient and constant toget...
Apr 19, 2026
