1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+～～1/9×1/10
=1-1/2+1/2-1/3+1/3-1/4+........+1/9-1/10
=1-1/10
=9/10
原式=1-1/2+1/2-1/3+1/3-1/4+……+1/9-1/10
=9/10
9/10
裂项相消
1×1/2+1/2×1/3+1/3×1/4+1/4×1/5+～～1/9×1/10
=1/1*2+1/2*3+1/3*4+～～1/9*10
=1-1/2+1/2-1/3+1/3-1/4～～1/9-1/10
=1-1/10
=9/10
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024