若数列{an}满足a1=1,a(n+1)=2的n次方*an,求数列通项公式an

2025-01-19 17:24:21
推荐回答(1个)
回答1:

a(n+1)=2^n*an
a(n+1)/an=2^n
累乘得
a2/a1*a3/a2*.....*a(n+1)/an=2^(1+2+...+n)
a(n+1)/a1=2^(1+2+...+n)=2^[n(1+n)/2]
a(n+1)=2^(1+2+...+n)=2^[n(1+n)/2]
an=2^[n(n-1)/2]