等差数列3 (25 9:16:40)

由于:Sm=Sn则有：Sm=(a1+am)m/2=[a1+a1+(m-1)d]m/2=ma1+m(m-1)d/2Sn=(a1+an)n/2=[a1+a1+(n-1)d]n/2=na1+n(n-1)d/2则：ma1+m(m-1)d/2=na1+n(n-1)d/2则有：(m-n)a1=(d/2)[(m-n)(1-n-m)]由于：m不等于n则：m-n不等于0则有：a1=(1-n-m)d/2则：S(m+n)=[a1+a(m+n)](m+n)/2=[a1+a1+(m+n-1)d](m+n)/2=0