1²+2²/1×2+2²+3²/2×3+······+2003²+2004²/2003×2004=
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 00:56:20
![1²+2²/1×2+2²+3²/2×3+······+2003²+2004²/2003×2004=](/uploads/image/z/169760-56-0.jpg?t=1%26%23178%3B%EF%BC%8B2%26%23178%3B%EF%BC%8F1%C3%972%EF%BC%8B2%26%23178%3B%EF%BC%8B3%26%23178%3B%EF%BC%8F2%C3%973%EF%BC%8B%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%C2%B7%EF%BC%8B2003%26%23178%3B%EF%BC%8B2004%26%23178%3B%EF%BC%8F2003%C3%972004%3D)
1²+2²/1×2+2²+3²/2×3+······+2003²+2004²/2003×2004=
1²+2²/1×2+2²+3²/2×3+······+2003²+2004²/2003×2004=
1²+2²/1×2+2²+3²/2×3+······+2003²+2004²/2003×2004=
是(1²+2²)/1×2+(2²+3²)/2×3+······+(2003²+2004²)/2003×2004=吗?
原式=1/2+2/1+2/3+3/2+3/4+4/3+……+2003/2004+2004/2003
=2/1+(1+3)/2+(2+4)/3+……+(2002+2004)/2003+2003/2004
=2*2003+2003/2004
=4007-1/2004
=8030027/2004