{an}的和Sn,{Sn}的和Tn,且Tn=2Sn-n²,求数列an

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{an}的和Sn,{Sn}的和Tn,且Tn=2Sn-n²,求数列an

{an}的和Sn,{Sn}的和Tn,且Tn=2Sn-n²,求数列an
{an}的和Sn,{Sn}的和Tn,且Tn=2Sn-n²,求数列an

{an}的和Sn,{Sn}的和Tn,且Tn=2Sn-n²,求数列an
由题有,Tn=2Sn-n^2 ①
∴Tn-1=2Sn-1-（n-1）^2②
①②相减,∴Sn=2an-2n+1③
Sn-1=2an-1-2(n-1)+1④
③④相减,∴an=2an-1+2
∴(an)+2=2(an-1+2)
∴｛(an)+2｝是以a1+2为首项,2为公比的等比数列,∴
an+2=(a1+2)*2^(n-1)
∴an=(a1+2)*2^(n-1)-2

Tn=2Sn-n² Tn-1=2Sn-1-(n-1)²
两式相减的 Sn=2an-n²+(n-1)² =Sn=2an-2n+1
sn-1=2an-1-2n+3 an=2an-2an-1-2可以化成 2an-1=an-2 两边同时加4 2an-1+4=an+2
形成一个等比数列，下面的你自己做的，电脑打起来很困难，记得考虑n=1的时候

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