Question

等差数列（an),前n项和为Sn.(1)Sm=n,Sn=m.求Sm+n的值（2）Sm=Sn(m不等于n)求Sm+n的值

Answer 1

设an=a+nd,d为公差

(1)

Sm=am+dm(m+1)/2=n

Sn=an+dn(n+1)/2=m

d=-(2m+2n)/mn

a=(m^2+n^2+mn+m+n)/mn

所以Sm+n

=(m+n)a+d(m+n)(m+n+1)/2

=-m-n

(2)

Sm=am+dm(m+1)/2=Sn=an+dn(n+1)/2

(m-n)(a+d(m+n+1)/2)=0

a+d(m+n+1)/2=0

Sm+n

=(m+n)a+d(m+n)(m+n+1)/2

=(m+n)(a+(m+n+1)/2)

=0