a1=1,Sn^2-Sn-1^2=an^3,求证数列an为等差数列,并求出通项公式(n>=2,且n属于整数)
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a1=1,Sn^2-Sn-1^2=an^3,求证数列an为等差数列,并求出通项公式(n>=2,且n属于整数)a1=1,Sn^2-Sn-1^2=an^3,求证数列an为等差数列,并求出通项公式(n>=2
a1=1,Sn^2-Sn-1^2=an^3,求证数列an为等差数列,并求出通项公式(n>=2,且n属于整数)
a1=1,Sn^2-Sn-1^2=an^3,求证数列an为等差数列,并求出通项公式(n>=2,且n属于整数)
a1=1,Sn^2-Sn-1^2=an^3,求证数列an为等差数列,并求出通项公式(n>=2,且n属于整数)
Sn^2-Sn-1^2=an^3,
(Sn-Sn-1)(Sn+Sn-1)=an^3,
an(Sn+Sn-1)=an^3,
(Sn+Sn-1)=an²
(Sn-1+Sn-2)=an-1²
两式相减an+an-1=an²-an-1²
an+an-1=(an+an-1)(an-an-1)
an-an-1=1
所以是a1=1,d=1的等差数列
an=a1+(n-1)d=1+n-1=n
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