MathDB

5

Part of 2008 Mathcenter Contest

Problems(3)

P_{2008}(2008) =? P_n(x)=P_{n-1}(x)+P_{n-1}(x-1), P_1(x)=2/x

Source: Mathcenter Contest / Oly - Thai Forum 2008 R2 p5 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

11/11/2022
Let P1(x)=1xP_1(x)=\frac{1}{x} and Pn(x)=Pn−1(x)+Pn−1(x−1)P_n(x)=P_{n-1}(x)+P_{n-1}(x-1) for every natural n n greater than 11. Find the value of P2008(2008)P_{2008}(2008).
(Mathophile)
algebrapolynomialrecurrence relation
a,b,c of 6 irrational exists usch that a+b,b+c,c+a are irrationals

Source: Mathcenter Contest / Oly - Thai Forum 2008 R1 p5 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

11/10/2022
There are 66 irrational numbers. Prove that there are always three of them, suppose a,b,ca,b,c such that a+ba+b,b+cb+c,c+ac+a are irrational numbers.
(Erken)
irrational numberalgebra
sum 1/(a^2+1) >= 3/2 if ab+bc+ca = 3

Source: Mathcenter Contest / Oly - Thai Forum 2008 R3 p5 https://artofproblemsolving.com/community/c3196914_mathcenter_contest

11/9/2022
Let a,b,ca,b,c be positive real numbers where ab+bc+ca=3ab+bc+ca = 3. Prove that 1a2+1+1b2+1+1c2+1≥32.\dfrac{1}{a^2+1}+\dfrac{1}{b^2+1}+\dfrac{1}{c^2+1}\geq\dfrac{3} {2}. (dektep)
algebrainequalities