Question

化简：1/（a-1）+1/{（a-1）(a+2)}+1/{(a-2)(a-3)``````+1/｛（a-99）(a-100)｝

Answer 1

1/（a-1）+1/{（a-1）(a-2)}+1/{(a-2)(a-3)``````+1/｛（a-99）(a-100)｝ =1/(a-1)+1/(a-1)-1/(a-2)+1/(a-2)-1/(a-3)+...+1/(a-99)-1/(a-100) =2/(a-1)-1/(a-100) =(a-199)/[(a-1)(a-100) 1/{（a-1）(a+2)}应该是1/{（a-1）(a-2)}吧?

Answer 2

1/(a-1)+1/(a-1)(a-2)+.....1/(a-99)(a-100) =1/(a-1)+[1/(a-2)-1/(a-1)]+....[1/(a-100)-1/(a-99)]=1/(a-1)+1/(a-2)-1/(a-1)+1/(a-3)-1/(a-2)+........+1/(a-100)-1/(a-99)=1/(a-100)