1x1/2 +2x1/3 +3x1/4+ …… +8x1/9 +9x1/10简便方法计算
问题描述：
1x1/2 +2x1/3 +3x1/4+ …… +8x1/9 +9x1/10简便方法计算
答
1x1/2 +2x1/3 +3x1/4+ …… +8x1/9 +9x1/10
=1-1/2+1-1/3+1-1/4+1-1/5+1-1/6+1-1/7+1-1/8+1-1/9+1-1/10
=9-(1/2+1/3+1/6+1/4+1/8+1/5+1/10+1/7+1/9)
=9-(1+3/8+3/10+16/63)
=9-(1+15/40+12/40+16/63)
=9-(1+27/40+16/63)
=9-1-(27*63+16*40)/40*63
=8-(1701+640)/2520
=8-2341/2520
=7又2520分之2341