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1h
comment How do I evaluate this:$\sum_{n=1}^{\infty}\frac{1}{n²}(e^x −1 −\frac{x}{1!} −\frac{x²}{2!}−\cdots\frac{x^n}{n!})$?
@zeraouliarafik If that was your first attempt how come you'd be surprised if it is convergent?
2h
comment Isomoprhic and equal symbol for abelian groups
Responsible use would at least require the groups to be canonically isomorphic, I suppose
11h
comment Why is this statement true?
So why don't you first expand what $f(t\xi_1,t\xi_2)$ is, as a function fo $t$?
1d
comment Construct an OR gate when missing input information
Are the random decisions of various $X$ independent?
1d
comment What's the meaning of an element that belongs to the same element?
@ExampleMo If we define $1=\{\emptyset\}$ and $2=\{\emptyset,\{\emptyset\}\}$ as usual, then $1\notin 1$, $1\in 2$, and $2\notin 2$. Also $1\subseteq 2$.
1d
comment What's the meaning of an element that belongs to the same element?
Such a set is called a Quine atom and its existence is negated in ZF(C) set theory by the Axiom of Regularity.
1d
comment Is there an algorithm to compute the degree of a polynomial?
It may be worth noting that for $k=\mathbb Z$ and if we additonally know $|a_i|\le M$ for all $i$, one can determine $f$ completely, that is: the degreee $n$ and all coefficients $a_i$ of $f(X)=a_0+a_1X+\ldots +a_nX^n$, in just two evaluations.
1d
comment Arc length function of a helix/spiral is convex?
These are unrelated
1d
comment Why is $\sum a_i \exp(b_i)$ always equal to $0$?
@KlausDraeger I suggest to add the condition $b_i(0)=0$ because any constant term can be replaced with a nonzero factor of $a_i$.
1d
comment Non-Cauchy products for series?
Yes you are treating $\sum b_n$ as a constant here. In a numerical application you would use unnecessarily many multiplications though ...
1d
comment Non-Cauchy products for series?
Yes, you can always transform $(\sum a_n) B=\sum (a_n B)$. But here that would give you a series of power series, not a power series ...
2d
comment Explain why this composite function is not allowed?
That makes the range of $g$ $[0,5]$, bu tthat doesn't matter, at least it is $\subseteq $ the domain of $f$
2d
comment Very difficult sequence
@calculus certainly the former, for the sake of being defined
Jul
4
comment How to calculate the Minimum of a set of Complex numbers?
You can't. It doesn't. There is none
Jul
4
comment For what values of $a$ does $\int_{0}^{1}(-\ln x)^adx$ converge?
For $t\gg 0$ we have $0<e^{-t}t^a<e^{-t/2}$
Jul
4
comment Prove that, in a simple graph G with n vertices and a edges, $2a \le n^2-n$
Count vertes-edge incidences (aka. hand-shakes) in two ways
Jul
3
comment set of all accumulation points of A is countable
Don't forget that $S(a)$ is not compact though :)
Jul
3
comment Class of matrices for wich $A^T=J-A.$
$A=\frac12J+B$ with $B$ antisymmetric.
Jul
3
comment Let $f(x) = [x], x \in [1,3]; \ \phi(x) = x , x \in [1,2]$ and $= 2x -2, x \in (2,3]$.show that $\int_1^3 f = \phi(3) - \phi (1)$
Actually, $\phi'(x)=1$ only for $x\in[1,2)$.
Jul
3
comment Let I be an ideal of a ring R. Prove that the quotient ring R/I is a commutative ring if and only if ab − ba ∈ I for all a, b ∈ R.
What is your question?