1,x1,x2...Xn,成等比数列,x1 x2..xn>0,x1*x2*...xn=?x1,x2...Xn,2成等比数列,x1 x2..xn>0,x1*x2*...xn=?
问题描述：
1,x1,x2...Xn,成等比数列,x1 x2..xn>0,x1*x2*...xn=?
x1,x2...Xn,2成等比数列,x1 x2..xn>0,x1*x2*...xn=?
答
当q=1时，x1*x2*...xn=1；
当q>0且q不等于1时，Xn=1*q(n)，n=0,1,2...
所以，x1*x2*...xn=1*q(1)1*q(2)...1*q(n)=1*q(1)*q(2)*...q(n)=q(1+2+...+n)=q(n(n+1)/2)
答
Tn=x1*x2*...xn
2Tn=1*x1*x2*...xn*2
2Tn=2*xn*xn-1.x1*1
4Tn²=2*2*..*2=2^(n+2)
Tn=2^(n/2)
答
设公比为q
则a1=1
a(n+2)=a1*q^(n+1)=2 即q^(n+1)=2 q=2^[1/(n+1)]
所以x1*x2*...xn=(a1*q)*(a1*q^2)*...*[a1*q^(n-1)]
=q^[1+2+...+(n-1)]
=q^[n(n-1)/2]
=2^[n(n-1)/2(n+1)]
=2^[(n²-n)/(2n+2)]