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Aug
24
comment Prove that the only numbers not expressible as a sum of consecutive positive integers takes the form $2^n$ for some $n \in \mathbb N$
Fixed thanks @MarkBennet. Could you elaborate on why writing this odd factor as a sum of consecutive integers helps me? As in the comment below I'm having trouble seeing where this gets me.
Aug
24
comment Prove that the only numbers not expressible as a sum of consecutive positive integers takes the form $2^n$ for some $n \in \mathbb N$
Sorry, I'm not sure I understand why writing $x = (m+(m+1)) \cdot 2^\alpha$ (if $x$ has one odd factor) helps me...
Feb
10
comment Buy more lottery tickets or more multipliers?
Actually I double with chance $1$ in $2$ so isn't it ($1/2 \cdot 2 + 1/3 \cdot 3 + \cdots$)? But thank you this is the way I was thinking about it
Jul
29
comment Flipping heads 10 times in a row
Alex, could you provide your closed form solution? I have recently asked this question myself and your question here was most helpful.
Dec
9
comment Proving that $\sum_j x^j$ is differentiable $(-1,1)$
Ah, so it converges on every interval $[-\beta, \beta]$ for $|\beta| < 1$? Many thanks for your help @EricAuld
Dec
8
comment Proving that $\sum_j x^j$ is differentiable $(-1,1)$
Yes but I am not sure how to show that $\sum_j (j+1)x^j$ converges to a finite number for $|x| < 1$?
Dec
8
comment Showing that $\sum_j e^{-jx}x^j$ converges uniformly
Hmm, thanks Mhenni! Any idea as to how I would actually compute the sum?
Nov
8
comment How to prove Riemann integrable with partitions
I understand, however, I am trying to prove this Riemann integrability from first principles, and so would like to find a way that involves a choice of partition rather than appeal to another theorem
Nov
7
comment Squares of differentiable functions
Sorry @dfeuer I meant $(f(x))^2$. Thanks Daniel Fischer!
Nov
5
comment Limit of metric of sequences
Ah! I have seen it: $|\rho(x_n,y_n) - \rho(x,y_n)| \leq |\rho(x_n,x) + \rho(x,y_n) - \rho(x,y_n)|$
Nov
5
comment Limit of metric of sequences
Hmm, in that case I suppose I'm just not quite sure how to show that something like $|\rho(x_n,y_n) - \rho(x, y_n)|$ can be made small?
Nov
5
comment Limit of metric of sequences
Ah yes I was unsure here whether I could use the absolute value metric $|\cdot|$ to prove convergence or whether I had to use a general $\rho$ to prove convergence. And $\rho$ is indeed a metric on $\mathbb R$
Sep
8
comment Showing that $(a_n^2)$ is Cauchy implies that $(a_n)$ is Cauchy
Ah! Precisely, thank you André
Jun
16
comment Checking an inductive proof on a combinatorial product
@coffeemath when you say "yes" are you confirming that I do indeed have this right? I have added the $k \geq 2$ condition thanks for this input. Regards.
Jun
13
comment Binomial coefficients equal to a prime squared
Never mind, I now see that you would need $2p \cdot (2p - 1) \cdots (p)(p-1)\cdots$. Thanks again
Jun
13
comment Binomial coefficients equal to a prime squared
I accepted Jyrki's answer, but I want to thank you for the referral to the paper, this is useful for the more general aspects of my project
Jun
13
comment Binomial coefficients equal to a prime squared
many thanks for this response. A neat proof! However I wonder if you could elaborate on why it is necessary that $2p \leq m$, and not the more trivial bound that $p^2 \leq m$?
Jun
5
comment Trying to prove an identity about a product
I will go down that route, thanks for your suggestions @wece
Jun
5
comment Trying to prove an identity about a product
@wece I thought that I should induct on $p$ and then perhaps have a "nested" induction on $n$ inside the proof. How can I induct on $n$ but still establish that it is only those above tuples that give me the desired dimension?
May
30
comment Number of possible pairs from $\{1,\dots, n\}$ with $i < j$
My mistake, it is in fact simply ${n \choose 2}$