等差数列若Sm=n,Sn=m,则Sm+n=-(m+n)为什么

Sm=a1m+m(m-1)d/2=n Sn=a1n+n(n-1)d/2=m 相减a1m+m(m-1)d/2-[a1n+n(n-1)d/2]=n-m a1(m-n)+(m+n-1)(m-n)d/2=n-m 两边除以m-na1+(m+n-1)d/2=-1 所以S(m+n)=a1(m+n)+(m+n)(m+n-1)d/2=-(m+n)