设数列an为等比数列,公比为q首项为a1 (1)计算A=1/a1+1/a2+..1/an,B=a1a2.an,C=a1+a2+.an(用a1,q表
问题描述:
设数列an为等比数列,公比为q首项为a1 (1)计算A=1/a1+1/a2+..1/an,B=a1a2.an,C=a1+a2+.an(用a1,q表
(2)求证B²=(C/A)^n
答
A=1/a1+1/a2+……+1/an=1/a1+(1/a1)×q^(-1)+(1/a1)×q^(-2)+……+(1/a1)×q^(-n)=(1/a1)[1-q^(-n)]/[1-q^(-1)]B=a1a2a3……an=(a1)^n×q^[1+2+3+……+(n-1)]=(a1)^n×q^[n(n-1)/2]C=a1+a2+...