已知数列{an}是等比数列,a2=2,a5=6,则a1a2+a2a3+a3a4+...+ana(n+1)=
问题描述:
已知数列{an}是等比数列,a2=2,a5=6,则a1a2+a2a3+a3a4+...+ana(n+1)=
2^(2n+1) -2/3
答
a1a2+...+ana(n+1)=Sa1a2+...+ana(n+1)=a1*a1*q+a2*a2*q...an*an*q=Sa2a2+...+anan=S/q-a1*a1=S/q-a2*a2/(q^2)a1a2+...+ana(n+1)=a2*a2/q+...+an*an/q+a(n+1)*a(n+1)/q=Sa2a2+...+anan=S*q-a(n+1)*a(n+1)=S*q-a2*a2*...