等差数列{an}{bn}的前n项和分别为Sn、Tn,且an:bn=2n-1:3n-1,则S2n+1:T2n+1=?
问题描述:
等差数列{an}{bn}的前n项和分别为Sn、Tn,且an:bn=2n-1:3n-1,则S2n+1:T2n+1=?
答
S(2n+1)=(2n+1)[a1+a(2n+1)]/2=(2n+1)a(n+1)
T(2n+1)=(2n+1)b(n+1)
an:bn=(2n-1):(3n-1)
a(n+1):b(n+1)=(2n+1):(3n+2)
S(2n+1):T(2n+1)=(2n+1)a(n+1):(2n+1)b(n+1)
=a(n+1):b(n+1)
=(2n+1):(3n+2)