MathDB

14

Part of 2018 Hanoi Open Mathematics Competitions

Problems(2)

polynomial P(k) =k/(k + 1), k=0,...,2017, p(2018)=? (HOMC 2018 Ind. p14)

Source:

1/31/2020
Let P(x)P(x) be a polynomial with degree 20172017 such that P(k)=kk+1P(k) =\frac{k}{k + 1}, ∀k=0,1,2,...,2017\forall k = 0, 1, 2, ..., 2017 . Calculate P(2018)P(2018).
algebrapolynomial
max T= (a-b)^{2018}+(b-c)^{2018}+(c-a)^{2018} (HOMC 2018 ind. sen14)

Source:

2/2/2020
Let a,b,ca,b, c denote the real numbers such that 1≤a,b,c≤21 \le a, b, c\le 2. Consider T=(a−b)2018+(b−c)2018+(c−a)2018T = (a - b)^{2018} + (b - c)^{2018} + (c - a)^{2018}. Determine the largest possible value of TT.
maximuminequalitiesalgebra