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Apr
23
comment if $X$ is a constant discrete random variable, then so is $E(X)$
The expectation of $X$ is in any case a number, "constant."
Apr
23
revised How many 5 digit numbers can be formed out of {1,2,3…,9} where a digit can repeat at most twice?
added 471 characters in body
Apr
23
answered How many 5 digit numbers can be formed out of {1,2,3…,9} where a digit can repeat at most twice?
Apr
23
comment Finding the limit of $\log(1+ax)/\log(1+x)$
@Wenty: Note that the answer for $a=0$ is different but easy.
Apr
23
revised What is the justification and intuition behind Muller's method's quadratic equation?
added 8 characters in body
Apr
23
comment Stuck on finding where $\sum_1^{\infty} (x+4)^{n}$ converges conditionally.
This is an endpoint issue only. We check, as you did, whether $\sum 1^n$ converges, and whether $\sum (-1)^n$ converges. Neither does, so we have conditional convergence nowhere. More interesting is $\sum \frac{x^n}{n}$. There we have absolute convergence in $(-1,1)$, conditional convergence at $x=-1$, divergence at $x=1$, so the interval of convergence is $[-1,1)$.
Apr
23
revised What is the justification and intuition behind Muller's method's quadratic equation?
added 343 characters in body
Apr
23
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 $(-5,-3)$.
Apr
23
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.
Apr
23
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.
Apr
23
answered What is the justification and intuition behind Muller's method's quadratic equation?
Apr
23
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.
Apr
23
reviewed Leave Open Big O comparison in asymptotic cases
Apr
23
reviewed Leave Open What is the best way to prove the mean value theorem
Apr
23
reviewed Leave Open Linear operator categories
Apr
23
reviewed Leave Open Convergence of $\sum\limits_{n=1}^{\infty} \frac{1}{nf(n)}$
Apr
23
reviewed Reopen The graph of $y=6\cos\theta+10\sin\theta$ would be a sinusoid if it were plotted…
Apr
23
comment Determining time it takes for two approaching cars to meet
The first solution is nicer. Probably the second solution is the intended one.
Apr
23
revised A proof about polynomial division
added 253 characters in body
Apr
23
answered A proof about polynomial division