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Sep
1
comment “Proof” that $1-1+1-1+\cdots=\frac{1}{2}$ and related conclusion that $\zeta(2)=\frac{\pi^2}{6}.$
Just to throw an additional spanner in the works: We can show that $$S=\sum_{k=0}^m (-1)^k = \frac{1}{2}(1+(-1)^m).$$ If we let $m\to\infty$, where $m$ is odd then using the formula gives $S=0$. If we let $m\to\infty$, where $m$ is even then $S=1$. The question is: which $m$ do we use? Odd, even? And, moreover, how come we don't get $1/2$ ??
Aug
28
asked Are these functions identical?
Aug
26
accepted Proof that $\zeta'(-2n)=(-1)^n\frac{(2n)!}{2(2\pi)^{2n}}\zeta(2n+1)$.
Aug
26
asked Proof that $\zeta'(-2n)=(-1)^n\frac{(2n)!}{2(2\pi)^{2n}}\zeta(2n+1)$.
Aug
22
comment Squared binomial paradox?
$(5-2)^2$ is not 49. It is $3^2=9$.
Aug
22
comment Proving $\frac\pi{22}\cos\frac\pi{22}+\frac{2\pi}{11}\cos\frac{5\pi }{22}+\frac{2\pi}{ 11}\cos\frac{9\pi}{22}+\frac\pi{22}\cos\frac{5\pi}{11}<\cdots$
Have you tried expanding as a power series to see what happens? Just a thought.
Aug
21
revised How to solve this and what is this number called?
changed symbol
Aug
21
comment How to solve this and what is this number called?
In addition to this answer, it is not know whether or not $\gamma$ can be expressed as a rational number.
Aug
21
suggested approved edit on How to solve this and what is this number called?
Aug
21
answered What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
Aug
20
comment General form for $2\int_{0}^{\infty} \frac{1-t^2}{(1+t^2)((a+b)t^2+a-b)} \mathrm dt$
This is not LaTeX as it stands. Please reformat.
Aug
19
revised Irrational number “test”?
added 12 characters in body
Aug
19
comment Irrational number “test”?
@ Erick thank you very much for your answer. I had an inkling my thoughts might be "on the right track", but clearly "hadn't got it quite right" !
Aug
19
comment Irrational number “test”?
@ Erick wow - I see that now: while $$\lim_{n\to\infty}\frac{u_n}{v_n} = \lim_{n\to\infty}\frac{n}{n+1}=1,$$ we have $$\lim_{n\to\infty}(n+1)\times 1-n=\lim_{n\to\infty} 1 = 1\neq 0.$$
Aug
19
comment Basic graphing - plot v = 10i +4
You're probably getting confused by a use of different variable names. You are probably familiar with $x$ and $y$ ? Just replace $v$ with $x$ and $i$ with $y$ to get $x=10y+4$, or rearranging $y=(x-4)/10=x/10-2/5.$ Since this is the equation of a line, let $x=0$ to get a $y$ value, then let $y=0$ to get an $x$ value. Plot these two coordinates and join them to get your line.
Aug
19
answered How can I bring $\sin(x)$ to the following form?
Aug
19
revised How can I bring $\sin(x)$ to the following form?
changed the title slightly
Aug
19
suggested approved edit on How can I bring $\sin(x)$ to the following form?
Aug
19
comment Irrational number “test”?
@ Erick but isn't this just the same as my original question, since $$\lim_{n\to\infty}v_n a-u_n=0 \iff \lim_{n\to\infty}a=\lim_{n\to\infty}\frac{u_n}{v_n}\iff a=\lim_{n\to\infty}\frac{u_n}{v_n},$$ and $u_n,v_n\to\infty$ as $n\to\infty$, $(u_n,v_n)=1$ ?
Aug
18
asked What is the asymptotic behaviour of $n^3 \log(\Gamma(1 + 1/n))$ as $n\to\infty$?