已知数列{an}的前n项和为Sn满足Sn-S(n-2)=3(-1/2)^(n-1)(n大于等于3)且S1=1,则S21=
问题描述:
已知数列{an}的前n项和为Sn满足Sn-S(n-2)=3(-1/2)^(n-1)(n大于等于3)且S1=1,则S21=
答
Sn-S(n-2)=3(-1/2)^(n-1)an+an-1=3(-1/2)^(n-1)a1=s1=1a3+a2=3(-1/2)^2=3*1/4a5+a4=3(-1/2)^4=3*(1/4)^2:a21+a20=3(-1/2)^20=3*(1/4)^10等式两边相加得s21=1+3[(1/4-(1/4)^11)/(1-1/4)]=2-(1/4)^10)...