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

题目

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

答案

1+(2-1/2)+(3-1+1/3)+(4-3/2+2/3-1/4)+……+(9-8/2+7/3-6/4+5/5 -4/6+3/7-2/8+1/9) =(1+2+...+9)-(1/2 +2/2 +...+8/2) +(1/3 +2/3+3/3+...+7/3)-(1/4 +2/4 +...+6/4)+(1/5 +2/5+...+5/5) -(1/6 +2/6+3/6+4/6)+(1/7+2/7+3/7)-(1/8+2/8)+1/9 =(1+2+...+9)-(1+2+...+8)/2 +(1+2+...+7)/3 -.+(1+2+3)/7 -(1+2)/8 +1/9 =45 -18+ 28/3 -21/4 +3- 5/3 +6/7 -3/8 +1/9 =30 +23/3 -45/8 +6/7 +1/9 =30+7-5+7/9 +6/7 -5/8