### Concours Centrale Supelec: mathématiques 2 PC

We end this series of problems for the 2023 PC competitive examination with this interminable subject, which goes off in just about every direction: polynomials, Python programming, integer series, summation of double series and finally probability.

In my opinion, there was no question that required a great deal of thought, rather a test of technical know-how, and in particular the calculation of sums, finite or infinite.

Question 14 may have posed problems for candidates

The justification for question 41 had to be rigorous.

Obviously, given the number of questions (41), the aim was to be particularly fast and efficient.

The most interesting part was Part I.B, whose central result was the formula \[\sum_{n=0}^{+\infty}n^kx^n = \frac{P_k(x)}{(1-x)^{k+1}} \], where \(P_k\) is a polynomial of degree k.

The coefficients of \(P_k\) can be calculated in the canonical basis of \(\mathbb{R}[X]\) using a program of asymptotic complexity \(O(k^2)\).

Solutions to the Maths 2 test on May 12 in the PC Centrale Supelec 2023 exam:

Problem set: