Q = \(\dfrac{1+x^4+x^8+...+x^{2020}}{1+x^2+...+x^{2022}}\)
Đặt A = 1 + \(x^4\) + \(x^8\) +...+ \(x^{2020}\)
Đặt B = 1 + \(x^2\) + ...+ \(x^{2022}\)
Thì Q = \(\dfrac{A}{B}\)
A = 1 + \(x^4\) + \(x^8\) + ...+ \(x^{2020}\)
A.\(x^4\) = \(x^4\) + \(x^8\) +....+ \(x^{2020}\) + \(x^{2024}\)
A.\(x^4\) - A = \(x^{2024}\) - 1
A = \(\dfrac{x^{2024}-1}{x^4-1}\)
B = 1 + \(x^2\) + \(x^4\) +...+ \(x^{2020}\) + \(x^{2022}\)
B.\(x^2\) = \(x^2\) + \(x^4\) +...+ \(x^{2020}\) + \(x^{2022}\) + \(x^{2024}\)
B\(x^2\) - B = \(x^{2024}\) - 1
B = \(\dfrac{x^{2024}-1}{x^2-1}\)
Q = \(\dfrac{\dfrac{x^{2024}-1}{x^4-1}}{\dfrac{x^{2024}-1}{x^2-1}}\)
Q = \(\dfrac{x^{2024}-1}{x^4-1}\) \(\times\)\(\dfrac{x^2-1}{x^{2024}-1}\)
Q = \(\dfrac{1}{x^2+1}\)
