若数列{An}为等比数列,且A1=2,q=(根号2)/2,则(A1)^2+(A2)^2+……+(A10)^2=(
问题描述:
若数列{An}为等比数列,且A1=2,q=(根号2)/2,则(A1)^2+(A2)^2+……+(A10)^2=(
1023/128
答
由数列{An}为等比数列可知数列{An^2}也为等比数列(An+1^2/An^2=q^2=1/2);
又A1^2=4
所以(A1)^2+(A2)^2+……+(A10)^2=1023/128