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Jul
1
comment Evaluation of $\sum_{n=1}^{\infty}\frac{2n-1}{2^n}$
That was meant for the asker, by the way.
Jul
1
comment Evaluation of $\sum_{n=1}^{\infty}\frac{2n-1}{2^n}$
Also don't forget that these formulas work when $n \ge 0$, but the series in the question has $n \ge 1$.
Jun
30
comment Confusion regarding change of variables in ODEs
It seems I just can't write comments today. I meant $g(x) = y(x+\pi)$.
Jun
30
comment Confusion regarding change of variables in ODEs
@Shuhaho: I'm sorry, I accidentally submitted that comment early and was going to fix it but I forgot. I understand that. What I was going to say is, what's the point of using a different variable name? Like you said; isn't it clearer to say "use $g(x) = g(x+\pi)$" instead of "use $t = x - \pi$"?
Jun
30
comment Confusion regarding change of variables in ODEs
That works. But what's the point then ofusing two different
Jun
23
comment Prove $\frac{\cos^2 A}{1 - \sin A} = 1 + \sin A$ by the Pythagorean theorem.
Do you know the identity $\cos^2 A + \sin^2 A = 1$?
Jun
21
comment How to derive compositions of trigonometric and inverse trigonometric functions?
@GitGud: Why shouldn't drawings count as proof? As long as you remember that the proof only works for angles smaller than $90^\circ$, they're perfectly good arguments.
Jun
21
comment Equivalence of Notation for Momentum Continuum
That it is an abuse of notation doesn't mean it's wrong. That's why it's called abuse and not misuse.
Jun
17
comment Differentiability of a function at a point to prove it differentiable everywhere on the given condition.
Consider the function that is $1$ at $0$ and $0$ everywhere else.
Jun
17
comment Why does derivation use lim? Alternative method possible!
What do you mean by relativity?
Jun
16
comment Graphing $\sin(|x|)$?
Is the sine of a positive number always positive?
Jun
16
comment Generelized Integral Convergence
@TheAnswer: It does solve your problem, you just didn't compute the limits correctly. Both are $-\infty$, therefore the limit doesn't exist and the integral doesn't converge.
Jun
14
comment Solving for $x$: $1=\frac{1}{x}+\frac{1}{1+\frac{1}{x}}+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}+\cdots$
Some quick calculations lead me to believe that the series does not converge, but I might be wrong.
Jun
14
comment Supposedly simple integral
This question may be relevant. Trying to solve the differential equation mentioned in the accepted answer leads to an integral similar to this one, so I'm not sure how useful it is.
Jun
13
comment Confused by $\Re(z)$ and closed contours, why isn't it the integral 0?
@Sharkos: Yes, I realized that after I posted the comment.
Jun
13
comment Confused by $\Re(z)$ and closed contours, why isn't it the integral 0?
Small tip: if you want us to tell you if there's anything wrong with your calculations, include them in the question.
Jun
4
comment How to calculate surface area of a curved plane?
It depends on the precise shape of the surface. Is this particular one supposed to be half a cylinder?
Jun
3
comment Prove or disprove: if $f$ and $fg$ are continuous then $g$ is continuous.
@vadim123: No, wait. If there was such a sequence, $f$ would not be continuous at $a$. You don't need $f$ to be continuous on an interval; I believe algebra of limits implies that if $f$ is continuous and non-zero at $a$, then so is $1/f$.
Jun
2
comment Prove or disprove: if $f$ and $fg$ are continuous then $g$ is continuous.
How can you deduce that $f$ must be continuous on an interval around $a$?
Jun
2
comment Prove that $x+e^{2x}=1$ have only one solution
$\ln(x+e^{2x}) \neq \ln x + \ln e^{2x}$.