已知等差数列{an}和{bn}满足an/bn=2n/3n+5 他们的前n项之和分别记为Sn和Tn 求S11/T11

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已知等差数列{an}和{bn}满足an/bn=2n/3n+5 他们的前n项之和分别记为Sn和Tn 求S11/T11
已知等差数列{an}和{bn}满足an/bn=2n/3n+5 他们的前n项之和分别记为Sn和Tn 求S11/T11

已知等差数列{an}和{bn}满足an/bn=2n/3n+5 他们的前n项之和分别记为Sn和Tn 求S11/T11
令an=2pn,bn=(3n+5)p=3np+5p
d1=an-a(n-1)=2pn-2p(n-1)=2p
d2=bn-b(n-1)=3np+5p-3(n-1)p-5p=3p
Sn=nan-n(n-1)d1/2=n[2pn-(n-1)*(2p)/2]=pn(n+1)
Tn=nbn-n(n-1)d2/2=n[3np+5p-(n-1)*(3p)/2]=pn[3n+5-(n-1)*(3/2)]=pn(3n/2+13/2)
S11/T11=(11+1)/(3*11/2+13/2)=24/46=12/23

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