Question

初一有理数计算题

1+(2/1-1/2)+(3/1-2/2+1/3)+(4/1-3/2+2/3-1/4)+...+(9/1-8/2+7/3-6/4+...+1/9)

Answer 1

把这题打开就可以发现如下规律:

1) 每组第一项

1+2/1+3/1+........+9/1= (1+9)*9/2 = 45

2) 一次类推2-9项:

-(0+1/2+2/2+3/2+........8/2) = -(1+8)*8/2/2=-18
+(1/3+2/3+.....7/3) = + (1+7)*7/3/2 = 28/3
-(1/4+2/4+.....6/4) = -(1+6)*6/4/2 = -21/4
+(1/5+2/5+.....5/5) = +(1+5)*5/5/2 = 3
-（1/6+2/6+3/6+4/6）= -5/3
+（1/7+2/7+3/7）= 6/7
-（1/8+2/8）= -3/8
+ 1/9

所以合计为：

= 45-18+28/3-21/4+3-5/3+6/7-3/8+1/9
= 30+1517/504 = 33+5/504 = 33(5/504)=33.01