等差数列,若Sm=n,Sn=m,则Sm+n=( )

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/23 20:59:41
等差数列,若Sm=n,Sn=m,则Sm+n=()等差数列,若Sm=n,Sn=m,则Sm+n=()等差数列,若Sm=n,Sn=m,则Sm+n=()Sm=a1m+m(m-1)d/2=n(1)Sn=a1n+

等差数列,若Sm=n,Sn=m,则Sm+n=( )
等差数列,若Sm=n,Sn=m,则Sm+n=( )

等差数列,若Sm=n,Sn=m,则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)

-(m+n)