1在等比數(shù)列{an}中,a9+a10=a(a不等于0）,a19+a20=b,則a99+a100等于?
a9+a10=a1*q^8+a1*q^9=a1*q^8*(1+q)=a ...q為公比
a19+a20=a1*q^18*(1+q)=b
so,兩式相除：q^10=b/a
a99+a100=a1*q^98*(1+q)=a1*q^8*(1+q)*q^90=a*q^90
=a*(q^10)^9=a*(b/a)^9
2設(shè)等比數(shù)列{an}的公比q=2,前n項(xiàng)和為Sn,則S4/a2=?
qSn+a1=Sn+a(n+1)
Sn=a1(1-q^n)/1-q
=a1(2^n-1)
S4/a2=a1*(2^4-1)/2a1=15/2