Question

已知數列{a_n}滿足a₁=2,a_n+1=2(1+)²a_n(n∈N^*),則數列{a_n}的通項公式為　　　　.

Answer 1

a_n=2ⁿ·n²

∵a_n+1=2(1+)²a_n,∴=,
∴a_n=··…···a₁
=··…···2
=2ⁿ·n²,
a₁=2也適合.