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2d
revised What is the justification and intuition behind Muller's method's quadratic equation?
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2d
comment Stuck on finding where $\sum_1^{\infty} (x+4)^{n}$ converges conditionally.
What you did, except that in addition we have to test for absolute convergence at the endpoints. In this case, we have that the sum of the absolute values diverges at the endpoints, so the interval of absolute convergence is $(-5,-3)$.
2d
comment Proving expressibility of integers as the difference of two squares.
For example let $m$ be odd, and let $ab=m$ (we can take $a=1,b=m$). We want to solve $x^2-y^2=m$. Set $x-y=a$, $x+y=b$ and solve for $x$ and $y$. We get $x=\frac{b+a}{2}$, $y=\frac{b-a}{2}$. Since $a$ and $b$ are odd, $x$ and $y$ are integers.
2d
comment Stuck on finding where $\sum_1^{\infty} (x+4)^{n}$ converges conditionally.
Absolute convergence means the sum of the absolute values converges. It implies convergence. The Ratio Test and Root Test tell you nothing about what happens at the endpoints, You could have absolute convergence at the endpoints, or divergence, or conditional convergence at one or both endpoints.
2d
answered What is the justification and intuition behind Muller's method's quadratic equation?
2d
comment Stuck on finding where $\sum_1^{\infty} (x+4)^{n}$ converges conditionally.
Your series converges absolutely for $-5\lt x\lt -3$, and diverges for $x\lt -5$ and for $x\gt -3$. It also diverges at $x=-5$ and $x=-3$, so it converges conditionally nowhere.
2d
reviewed Leave Open Big O comparison in asymptotic cases
2d
reviewed Leave Open What is the best way to prove the mean value theorem
2d
reviewed Leave Open Linear operator categories
2d
reviewed Leave Open Convergence of $\sum\limits_{n=1}^{\infty} \frac{1}{nf(n)}$
2d
reviewed Reopen The graph of $y=6\cos\theta+10\sin\theta$ would be a sinusoid if it were plotted…
2d
comment Determining time it takes for two approaching cars to meet
The first solution is nicer. Probably the second solution is the intended one.
2d
revised A proof about polynomial division
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2d
answered A proof about polynomial division
2d
comment Does this limit exist finitely?
Same geometric series approximation, limit corrected.
2d
revised Does this limit exist finitely?
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2d
answered Does this limit exist finitely?
2d
comment Requesting help on understanding series
What is the tangent of a series?
2d
comment How to take the derivative of this
Do you know how to find the derivative?
2d
answered Proof involving primitive Pythagorean triples