已知数列an中,a1=2,an+1=4an-3n+1,bn=an-n,求证数列bn为等比数列,求an前n项和
<p>问题：已知数列an中,a1=2,an+1=4an-3n+1,bn=an-n,求证数列bn为等比数列,求an前n项和<p>答案：↓↓↓<p class="nav-title mt10" style="border-top:1px solid #ccc;padding-top: 10px;">陈跃斌的回答：<div class="content-b">网友采纳 an+1=4an-3n+1 an+1-n-1=4an-4n an+1-（n+1)=4(an-n) /(an-n)=4 所以an-n是等比数列 bn=an-n,所以bn是等比数列,b1=1,q=4 Sbn=(4^n-1)/3 San=Sbn-(1+2+3.+n) =(4^n-1)/3-(1+n)*n/2 =(4^n-1)/3-(n+n^2)/2
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