a₂-a₁=2¹，a₃-a₂=2²，a₄-a₃=2³，…依此类推可得a_n-a_n-1=2^n-1
∴a₂-a_1⁺a₃-a_2⁺a₄-a_3…⁺a_n-a_n-1⁼a_n^-a_1⁼2^1₊2^2₊2^3_+…+2^n-1₌2ⁿ-2
∴a_n^-a_1⁼2ⁿ-2，a_n⁼2ⁿ-1
故答案为2ⁿ-1