计算1/1×2+1/2×3＋1/3×4+1/4×5+……+1/2011×2012=?
问题描述：
计算1/1×2+1/2×3＋1/3×4+1/4×5+……+1/2011×2012=?
答
1/1×2+﹛1/2×﹙1/3＋2/3﹚﹜×3+﹛1/3×﹙1/4+3/4﹚×4+......+﹛1/2011×﹙1/2012+2011/2012﹚﹜×2012
＝2+﹙1/2-1/3+1/3﹚×3+﹙1/3-1/4+1/4﹚×4+............+﹙1/2011-1/2012+1/2012﹚×2012
＝1-1/2012
=2011/2012
答
简单的很 1/1×2=1-1/2 1/（2×3）=1/2-1/3 …… 1/2011×2012=1/2011-1/2012
所以1/1×2+1/2×3＋1/3×4+1/4×5+……+1/2011×2012=1-1/2+1/2-1/3+……+1/2011-1/2012
= 1-1/2012
=2011/2012
答
1/1×2+1/2×3＋1/3×4+1/4×5+……+1/2011×2012
=1/1-1/2+1/2-1/3+1/3-1/4+.+1/2011-1/2012
=1-1/2012
=2011/2012