设等比数列{an}的公比为q,求证a1a2...an=a1^nq^n(n+1)/2.

问题描述:

设等比数列{an}的公比为q,求证a1a2...an=a1^nq^n(n+1)/2.

an=a1*q^(n-1)
a1a2...an
=a1*a1q*a1q^2*a1q^3*……*a1q^(n-1)
=(a1)^n*q^(1+2+3+……+(n-1))
=(a1)^n*q^n(n-1)/2 注:不是n(n+1)