a1=1 an+1=an+2n 求an解析式 要过程,大谢
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a1=1 an+1=an+2n 求an解析式 要过程,大谢
a1=1 an+1=an+2n 求an解析式 要过程,大谢
a1=1 an+1=an+2n 求an解析式 要过程,大谢
因为an+1-an=2n
则有a2-a1=2
a3-a2=4
a4-a3=6
……
an-a(n-1)=2(n-1)
将各式两边分别相加可得
an-a1=2+4+6+8+ ……+2(n-1)=(2+2n-2)(n-1)/2=n(n-1) (n≥2)
而a1=1 所以an= n(n-1)+1 (n≥2)
当n=1时,上式也成立
所以an= n(n-1)+1 (n为正整数)
a(n+1)-a(n)=2n ;
a(n) -a(n-1)=2(n-1);
: :
a(2)- a(1)= 2
上式求合
a(n)-a(1)=2(1+2+3+……+n-1)=n(n-1)
a(n)=n(n-1)+1
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