关于等比数列的概念与通项公式的数学题数列1,X1,X2,…X2n,2是等比数列,试求X1*X2*…*X2n的值

Question

关于等比数列的概念与通项公式的数学题
数列1,X1,X2,…X2n,2是等比数列,试求X1*X2*…*X2n的值

Answer 1

共计2n+2项
=>
A(2n+2)=2
=>
A1*q^(2n+1)=2
=>
q^(2n+1)=2
=>
q=2^(1/(2n+1))
x1*x2*x3...*x2n
=q*(q^2)(q^3)...q(^(2n))
=q^(1+2+3+...2n)
=q^((2n+1)*n)
=2^((2n^2+n)/(2n+1))
=2^n