有沒有什麼很快的方法可以算出這題答案？

Sol
2/[k(k+1)(k+2)]=a/k+b/(k+1)+c/(k+2)
2=a(k+1)(k+2)+bk(k+2)+ck(k+1)
When k=0
26=a*1*2
a=1
When k=－1
2=b*(－1)*1
b=－2
when k=－2
2=c*(－2)*(－1)
c=1
2/[k(k+1)(k+2)]=1/k-2/(k+1)+1/(k+2)
So
2/(1*2*3)+2/(2*3*4)+2/(3*4*5)+…+2/(97*98*99)+2/(98*99*100)
=(1/1－2/2+1/3)+(1/2－2/3+1/4)+(1/3－2/4+1/5)+(1/4－2/5+1/6)+…
+(1/95－2/96+1/97)+(1/96－2/97+1/98)+(1/97－2/98+1/99)+(1/98－2/99+1/100)
=1/1－1/2－1/99+1/100
=(9900－4950－100+99)/9900
=4949/9900
(B)