MathematicsHard64×since 2002Q3000Let n ≥\ge≥ 5 be an integer. If 9^n −-− 8n −-− 1 = 64α\alphaα and 6^n −-− 5n −-− 1 = 25β\betaβ, then α\alphaα −-− β\betaβ is equal toA1 + ^nC₂ (8 −-− 5) + ^nC₃ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 1 −-− 5^n −-− 1)B1 + ^nC₃ (8 −-− 5) + ^nC₄ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 2 −-− 5^n −-− 2)C^nC₃ (8 −-− 5) + ^nC₄ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 2 −-− 5^n −-− 2)D^nC₄ (8 −-− 5) + ^nC₅ (8² −-− 5²) + ...... + ^nC_n (8^n −-− 3 −-− 5^n −-− 3)Check answerSkip