MathDB

A real number sequence

a_1, \cdots ,a_{2021}

satisfies the below conditions.

a_1=1, a_2=2, a_{n+2}=\frac{2a_{n+1}^2}{a_n+a_{n+1}} (1\leq n \leq 2019)

Let the minimum of

a_1, \cdots ,a_{2021}

m

, and the maximum of

a_1, \cdots ,a_{2021}

M

. Let a 2021 degree polynomial

P(x):=(x-a_1)(x-a_2) \cdots (x-a_{2021})

|P(x)|

is maximum in

[m, M]

when

x=\alpha

. Show that

1<\alpha <2

P5