数列1,3,6,10…… 怎么求数列1,3,6,10……的求和公式?

~ 因为an-a(n-1)=n,n=2,3,4,.,所以
an=a1+(a2-a1)+(a3-a2)+...+(an-a(n-1))
=1+2+3+...+n
=n(n+1)/2
=(1/2)(n^2+n)(n=1,2,3,...)
所以
Sn＝(1/2)[(1^2+2^2+3^3+...+n^2)+(1+2+3+...+n)]
=(1/2)[(1/6)n(n+1)(2n+1)+n(n+1)/2]
=n(n+1)(n+2)/6.