Question

已知等比数列{an}的通项公式为an=(1/3)^n,则a1^2+a2^2+…+a10^2=

Answer 1

an=(1/3)^n,则(an)^2 = ((1/3)^n)^2 = (1/9)^n

数列{ (an)^2}是首项为1/9,公比为1/9的等比数列

a1^2+a2^2+…+a10^2= 1/9×（1-1/9^10)/(1-1/9) = 1/8*(1-1/9^10)