等差数列{an}中,Sm=n,Sn=m(m≠n),求证Sm+n=-(m+n)

Question

等差数列{an}中,Sm=n,Sn=m(m≠n),求证Sm+n=-(m+n)

Answer 1

Sm=a1m+m(m-1)d/2=n
Sn=a1n+n(n-1)d/2=m
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
a1+(m+n-1)d/2=-1
Sm+n=a1(m+n)+(m+n)(m+n-1)d/2=-(m+n)本回答被提问者采纳

Answer 2

尽力了