Question

一道求数列通项公式的题目~已知数列{An}满足A1=12^(n-1)An=A(n-1)(n属于正整数,n大于等于2)求数

Answer 1

因为2^(n-1)An=A(n-1)

所以An/A(n-1)=2^(n-1)

所以An = (An/An-1)*(An-1/An-2)*(An-2/An-3)*…*(A2/A1)* A1

= 1/(2^n-1)*1/(2^n-2)*1/()2^n-3 … 1/2^1 * 1

= 1/(2^n-1*2^n-2*2^n-3 … 2^1)

= 1/2^(1+2+3+…+n-1)

= 1/2^[n(n-1)/2]

所以,最后An = 1/2^[n(n-1)/2] （n属于正整数）

上述中n-1 n-2等均为上标和下标.