神马作文网超难计算题,天才留步!
来源：学生作业帮 编辑：神马作文网作业帮 分类：数学作业 时间：2024/10/04 20:32:29
超难计算题,天才留步!
1+1/3+1/6+1/10+…+1/2009×1004=?
quickly quickly quickly
1+1/3+1/6+1/10+…+1/2009×1004=?
quickly quickly quickly
1+1/3+1/6+1/10+.+1/(2009×1004)
=2/2+2/(2×3)+2/(3×4)+2/(4×5)+.+2/(2008×2009)
=2×〔1/2+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(2008×2009)]
=2×(1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2008-1/2009)
=2×(1-1/2009)
=2×2008/2009
=4016/2009
=2/2+2/(2×3)+2/(3×4)+2/(4×5)+.+2/(2008×2009)
=2×〔1/2+1/(2×3)+1/(3×4)+1/(4×5)+.+1/(2008×2009)]
=2×(1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2008-1/2009)
=2×(1-1/2009)
=2×2008/2009
=4016/2009