∵等差数列{an},第n项an=a1+(n-1)d,前n项和Sn=(a1+an)n/2
∴第2n-1项a2n-1=a1+(2n-1-1)d=a1+2(n-1)d
∴前2n-1项和a1+a2+a3……+a2n-1=S2n-1=(a1+a2n-1)(2n-1)/2=[a1+a1+2(n-1)d](2n-1)/2
=[a1+(n-1)d](2n-1)=an(2n-1)
∴[a1+a2+a3……+a2n-1]/(2n-1)=an