a1=1/2 an+1=an+1/4n^2-1 则该数列的通项公式是
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a1=1/2 an+1=an+1/4n^2-1 则该数列的通项公式是
a1=1/2 an+1=an+1/4n^2-1 则该数列的通项公式是
a1=1/2 an+1=an+1/4n^2-1 则该数列的通项公式是
an+1=an+1/4n^2-1,
则当n>=2时:
an+1-an=1/4n^2-1=1/[(2n-1)(2n+1)]=1/2*[1/(2n-1)-1/(2n+1)],
所以有:
an-an-1=1/2*[1/(2n-3)-1/(2n-1)]
.
.
a2-a1=1/2*[1-1/3]
等式左右均相加,得到
an-a1=1/2*[1-1/(2n-1)]
an=a1+1/2*[1-1/(2n-1)]
=1/2+1/2-1/(4n-2)
=1-1/(4n-2)
=(4n-3)/(4n-2)
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