Question

[Lê Minh Tuấn]

2.Cho đa thức R(x)=x²-2x.Tính giá trị của biểu thức 

\(S=\dfrac{1}{R\left(3\right)}+\dfrac{1}{R\left(4\right)}+\dfrac{1}{R\left(5\right)}+...+\dfrac{1}{R\left(2022\right)}+\dfrac{1}{2.2023}\)

Giaỉ chi tiết

Answer 1

[tuan manh]

cái cuối là \(R\left(2023\right)\) hay 2.2023 vậy bạn ?

Answer 2

[Nguyễn Lê Phước Thịnh]

Sửa đề: 1/R(2023)

R(3)=1*3

R(4)=2*4

R(5)=3*5

...

R(2022)=2020*2022

R(2023)=2021*2023

=>\(S=\dfrac{1}{1\cdot3}+\dfrac{1}{3\cdot5}+...+\dfrac{1}{2021\cdot2023}+\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+...+\dfrac{1}{2020\cdot2022}\)

\(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{2021\cdot2023}+\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+...+\dfrac{2}{2020\cdot2022}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2021}-\dfrac{1}{2023}+\dfrac{1}{2}-\dfrac{1}{4}+...+\dfrac{1}{2020}-\dfrac{1}{2022}\right)\)

\(=\dfrac{1}{2}\cdot\left(\dfrac{2022}{2023}+\dfrac{505}{1011}\right)\simeq0.7496\)