计算(1/2+1/3+……+1/2005)(1+1/2+1/3……+1/2004)-(1+1/2……+1/2005)(1/2+1/3……+1/2004)

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/17 16:04:24

计算(1/2+1/3+……+1/2005)(1+1/2+1/3……+1/2004)-(1+1/2……+1/2005)(1/2+1/3……+1/2004)
计算(1/2+1/3+……+1/2005)(1+1/2+1/3……+1/2004)-(1+1/2……+1/2005)(1/2+1/3……+1/2004)

计算(1/2+1/3+……+1/2005)(1+1/2+1/3……+1/2004)-(1+1/2……+1/2005)(1/2+1/3……+1/2004)
(1/2+1/3+……+1/2005)(1+1/2+1/3……+1/2004)-(1+1/2……+1/2005)(1/2+1/3……+1/2004)
=(1/2+1/3+……+1/2004)(1+1/2+1/3……+1/2004)+1/2005*(1+1/2+1/3……+1/2004)-(1+1/2……+1/2004)(1/2+1/3……+1/2004)-1/2005*(1/2+1/3……+1/2004)
=1/2005*(1+1/2+1/3……+1/2004)-1/2005*(1/2+1/3……+1/2004)
=1/2005[1+1/2+1/3……+1/2004-(1/2+1/3……+1/2004)]=1/2005