1/1X(x+1) + 1/(x+1)(x+2)+1/(x+2)(x+3)……+1/(x+1998)(x+1999) 当x=1时这个代数式的值如何做

问题描述:

1/1X(x+1) + 1/(x+1)(x+2)+1/(x+2)(x+3)……+1/(x+1998)(x+1999) 当x=1时这个代数式的值如何做

裂项.1/x(x+1)=1/x-1/(x+1),1/(x+1)(x+2)=1/(x+1)-1/(x+2),以此类推……
所以最后原式=1/x-1/(x+1999),代入x=1得1999/2000