is a nonnegative integer, evaluate 
.
be a 
be a prime number?
![\[
f_k(x) = 1 + 2x + 3x^2 + \dots + (k+1)x^k,
\]](http://latex.artofproblemsolving.com/f/3/5/f35ea75e6415a63a40fb2c3c95fa5801e6fb891f.png)
![\[
\begin{vmatrix}
f_0(1) & f_1(1) & f_2(1) & \dots & f_{2023}(1) \\
f_0(2) & f_1(2) & f_2(2) & \dots & f_{2023}(2) \\
\vdots & \vdots & \vdots & \ddots & \vdots \\
f_0(2024) & f_1(2024) & f_2(2024) & \dots & f_{2023}(2024)
\end{vmatrix}
= \prod_{k=1}^{2024} k!.
\]](http://latex.artofproblemsolving.com/4/7/f/47ff41069b9444fe794076787b8890352929047a.png)
is defined by the conditions
and 
for a set of indices 
.
satisfying the equation![\[
(I_p + A)^n = B^n + C^n.
\]](http://latex.artofproblemsolving.com/2/d/7/2d75d47203353160ccac356251659bd16a4cb5c8.png)
be all of the extrem points of 
.
be two complex numbers such that 
and 
,
.
satisfy the relation 
.
and 
are invertible.
I can prove that the sequence 
is convergent by monotone bounded convergence theorem.
Y by RainbowJessa
Several posts have been made about this years before, but the office hours banner hasn't appeared yet even though I refreshed the page multiple times. It has been 50 minutes since when office hours should have started and no mods have responded to a question I posted 3 hours ago (relative to last edit). Can others confirm?
This post has been edited 2 times. Last edited by GAMER100, Mar 25, 2025, 12:19 AM
