Đáp án A
Ta có tan π 8 = 2 − 1 suy ra u n + 1 = u n + tan π 8 1 − tan π 8 . u n
Đặt tan φ = 2 suy ra u 1 = tan φ → u 2 = u 1 + tan π 8 1 − tan π 8 . u 1 = tan φ + tan π 8 1 − tan φ . tan π 8 = tan φ + π 8
Do đó u 3 tan φ + 2. π 8 → u n tan φ + n . π 8
Vậy u 2018 = tan φ + 2017. π 8 = tan φ + π 8 = u 2 = 2 + 2 − 1 1 − 2 2 − 1 = 7 + 5 2