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)

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 = 452) 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 =...