求(r+3)/[r(r+1)(r+2)]的前n项和Sn
问题描述：
求(r+3)/[r(r+1)(r+2)]的前n项和Sn
答
(r+3)/[r(r+1)(r+2)]=a/r+b/(r+1)+c/(r+2)r+3=a(r^2+3r+2)+b(r^2+2r)+c(r^2+r)=r^2(a+b+c)+r(3a+2b+c)+2aa+b+c=03a+2b+c=12a=3,a=1.5b+c=-1.52b+c=-3.5b=-2,c=0.5.5,a=1.5Sn各项如上分解,并相互抵消后得：Sn=1.5-2/2...