1/5×1/6 +1/6 ×1/7 +1/7 ×1/8 +1/8 ×1/9 +1/9 ×1/10的简算1/5×1/6 +1/6 ×1/7 +1/7 ×1/8 +1/8 ×1/9 +1/9 ×1/10的简便算法,
问题描述：
1/5×1/6 +1/6 ×1/7 +1/7 ×1/8 +1/8 ×1/9 +1/9 ×1/10的简算
1/5×1/6 +1/6 ×1/7 +1/7 ×1/8 +1/8 ×1/9 +1/9 ×1/10的简便算法,
答
1/5×1/6 +1/6 ×1/7 +1/7 ×1/8 +1/8 ×1/9 +1/9 ×1/10=(1/5-1/6) +(1/6 -1/7) +(1/7 -1/8)0 +(1/8 -1/9) +(1/9 -1/10)=1/5-1/10=1/10
有个公式是(1/n).(1/(n+1))=1/n-1/(n+1)
答
原式=(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/5-1/10
=1/10
答
原式=1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10
=1/5-1/10
=1/10