(1)20042004*20042003-20042005*20042002 (2)1又1/5+3又1/35-5又1/63+7又1/99+9又1/143+11又1/195
问题描述:
(1)20042004*20042003-20042005*20042002 (2)1又1/5+3又1/35-5又1/63+7又1/99+9又1/143+11又1/195
(3)1+/12+(1/3+2/3)+(1/4+2/4+3/4)+…+(1/50+2/50+…+49/50
答
(1)20042004*20042003-20042005*20042002
=20042004*(20042004-1)-(20042004+1)*(20042004-2)
设m=20042004,则
(1)=m(m-1)-(m+1)(m-2)
=m^2-m-m^2+m+2
=2
(2)1又1/5+3又1/35+5又1/63+7又1/99+9又1/143+11又1/195
=1+1/5+3+1/35+5+1/63+7+1/99+9+1/193+11+1/195
=1+3+5+7+9+11+1/5+1/2(1/7-1/9)+1/2(1/9-1/11)+1/2(1/11-1/13)+1/2(1/13-1/15)
=26+1/5+1/2(1/7-1/15)
=26又5/21