Question

Sn为等差数列的前n项和,Sn=m,Sm=n,求:Sm+n

Answer 1

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)