设等差数列{an}与{bn}的前n项和分别为Sn和Tn,且Sn/Tn=(3n+2)/(2n+1),limn→∞an/bn=
问题描述:
设等差数列{an}与{bn}的前n项和分别为Sn和Tn,且Sn/Tn=(3n+2)/(2n+1),limn→∞an/bn=
答
设an=a1+(n-1)d1,bn=b1+(n-1)d2∴ Sn=na1+n(n-1)d1 /2Tn=nb1+n(n-1)d2 /2∴ lim (n-->∞)Sn/Tn=lim (n-->∞) [a1+(n-1)d1 /2]/[b1+(n-1)d2 /2]= d1/d2∵ Sn/Tn=(3n+2)/(2n+1)∴ lim (n-->∞)Sn/Tn=3/2即 d1/d2=3/2∴...