求数列的求和公式-1,8,-17,32,-49,72

-1+8=7,-17+32=15,-49+72=23,....
-1,8+(-17)=-9,32+(-49)=-17,....
a1=-1,a2=8,a3=-17,a4=32,a5=-49,a6=72,....
Sn=a1+a2+a3+...+an
当n为偶数时,
Sn=(-1+8)+(-17+32)+(-49+72)+...
=7+15+23+...+{7+[(n/2)-1]*8}
=7n/2+(n/2)[(n/2)-1]*8/2
=7n/2+n²-2n=n²+3n/2
当n为奇数时,
Sn=-1+(8-17)+(32-49)+...
=-1-9-17-...-{1+[(n+1)/2-1]*8}
=-{(n+1)/2+(n+1)/2[(n+1)/2-1]*8/2}
=-n²-n/2+1/2