(1/2+1/3+...1/2005)乘(1-1/2+1/3+...1/2004)-(1+1/2+...1/2005)乘(1/2+_数学解答

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

人气：225 ℃　时间：2019-08-20 03:39:50

解答

令a=1/2+1/3+...1/2004
原式=(a+1/2005)(1+a)-(1+a+1/2005)a
=a(1+a)+1/2005(1+a)-a(1+a)-1/2005a
=1/2005(1+a)-1/2005a
=1/2005+1/2005a-1/2005a
=1/2005