Sn为等差数列的前n项和,Sn=m,Sm=n,求:Sm+n

Sm=a1m+m(m-1)d/2=n (1)
Sn=a1n+n(n-1)d/2=m (2)
(1)-(2)
a1(m-n)+(m+n-1)(m-n)d/2=n-m
a1+(m+n-1)d/2=-1
a1=-1-(m+n-1)d/2
Sm+n=a1(m+n)+(m+n)(m+n-1)d/2
=[-1-(m+n-1)d/2](m+n)+(m+n)(m+n-1)d/2
=-(m+n)