WH060425
幼苗
共回答了10个问题采纳率:100% 举报
∵函数f(x)=a1+a2x+a3x2+…+anxn-1,f(0)=1/2 ,
∴a1=1/2 ,
∵f(1)=n2•an,
∴a1+a2+a3+…+an=n2•an,
又∵an=Sn-Sn=n2•an-(n-1)2•an-1,
∴(n2-1)an=(n-1)2•an-1(n≥2),
an/an-1 =n2-1/(n-1)2 =n+1/n-1
a2/a1 •a3/ a2 •a4 /a3 …an /an-1 =1/3 ×2/4 ×…×n-2/n ×n-1/n+1 ,
an/an-1 =1/3 ×2/4 ×…×n-2/n ×n-1/n+1 ,
∴an=1/n(n+1) ,
1年前
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