来自马国敬的问题
1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
1回答
2020-03-30 10:27
1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)
利用:1/(x-(n+1))-1/(x-n)=1/(x-n)(x-(n+1))来解如:1/(x-2)-1/(x-1)=1/(x-1)(x-2)所以:1/(x-1)+1/(x-1)(x-2)+...+1/(x-2010)(x-2011)=1/(x-1)+1/(x-2)-1/(x-1)+……+1/(x-2011)-1/(x-2010)=1/(x-2011)...