(1/2+1/3+...+1/2005)乘(1+1/2+...+1/2004)-(1+1/2+...+1/2005)(1/2+1/3+...+1/2004)

问题描述:

(1/2+1/3+...+1/2005)乘(1+1/2+...+1/2004)-(1+1/2+...+1/2005)(1/2+1/3+...+1/2004)

依题意得: 令t=1/2+1/3…+1/2004,则原试=(t+1/2005)*(1+t)-(1+t+1/2005)*t =t+t平方+1/2005+1/2005*t-t平方-2006/2005*t =1/2005