等差数列求和公式!为什么Sn=na1+n(n-1)d/2会等于Sn=dn^2/2+(a1-d/2)n?

Question

等差数列求和公式!
为什么
Sn=na1+n(n-1)d/2 会等于Sn=dn^2/2+(a1-d/2)n?

Answer 1

Sn=na1+n(n-1)d/2展开得：
S n=na1+1/2*n^2d-1/2*nd=dn^2/2+(a1-d/2)n