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Self-learning mathematics. Many thanks to those who make time to help others on the site.


Jun
2
comment Showing existence of an element with order $p$
Do you mind explaining further? I'm still not sure what to do.
May
27
comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$
but $r$ is indexed
May
27
comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$
In my text, I have an identity $\sum_{r\geq 0} \binom{r + n}{r} x^r = 1/(1-x)^{n+1}$ This may be the cause of my confusion, but is this identity correct and is it equivalent to the one you used?
May
27
comment Proving $\sum_{m=0}^M \binom{m+k}{k} = \binom{k+M+1}{k+1}$
Is there a typo in the second equation (first sum)? I believe $k$ should be indexed.
May
26
comment Finding the values of $z$ s.t. $\sum_{n=0}^{\infty} \left( \frac{z}{1+z} \right)^n$ is convergent
yeah, I got the same thing, but I just didn't express the final step like that. Does it matter though?
May
26
comment Finding the values of $z$ s.t. $\sum_{n=0}^{\infty} \left( \frac{z}{1+z} \right)^n$ is convergent
$z > 1-\bar{z}$?
May
17
comment Are there any series whose convergence is unknown?
Out of curiosity, what makes this a "joke" answer?
May
14
comment Finding asymptotes of exponential function and one-sided limit
@Mhenni Why are the first two terms of the taylor series expansion enough to find the asymptote? Certainly there are functions where the first two terms wouldn't suffice to give an accurate approximation.
May
14
comment What are the limits and asymptotes of $f(x)=x+\frac{1}{x}$?
@Garmen1778 I'm not sure if you were implying that there was a horizontal asymptote or not, but in case there's any ambiguity, there are no horizontal asymptotes.
May
12
comment Using $\gcd(a,b)$ to find gcd of other values $\gcd(a^2,b)$ and $\gcd(a^3,b)$
Why is $b = p^{50}m$?
May
3
comment Is there something faulty about this statement?
Yeah, but when they used $k$ in both, it reads that the $k$'s are going to be the same. Is this sort of thing standard notation?
May
3
comment Trig and algebra problem: Finding sides of a triangle
by expanding the whole thing on the RHS?
May
3
comment Trig and algebra problem: Finding sides of a triangle
I was able to get that, but I don't know what to do with it
May
2
comment Rudin or Apostol
@BrianM.Scott When you say Apostol covers more material, do you mean that he's just more explicit in his explanations or he covers all the topics and theorems that Rudin does, plus more?
Apr
26
comment Show that there is no rational number $r=m/n$ such that $r^3=3$
@EricNaslund Do you mean as long as $n\geq 2$ is an integer?
Apr
25
comment Show that there is no rational number $r=m/n$ such that $r^3=3$
@ThomasAndrews Does it make a difference that this is cubed root?
Apr
25
comment Proving a complex equality
So for the trivial case, you can't use the quotient you've set $z$ equal to?
Apr
23
comment Proving a complex equality
I'm aware of that answer, but I'm looking for an algebraic answer simply because that wouldn't come to me immediately. How did you see that it was an ellipse? I ask because it's not in the familiar form that you see in conic sections of calculus.
Apr
13
comment Finding a closed form expression for this sum
How do you know that the 2nd term is equal to $(1/\sqrt{1-4x})^2$?
Apr
13
comment Finding a closed form expression for this sum
@MarcvanLeeuwen How did you search for that? I didn't know how to search for it because there's no specific name or term associated with it. O.w. I'd just have to look through all the results one at a time.