Question

1/1+(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)计算

Answer 1

1/1+(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+5/5-4/6+3/7-2/8+1/9
=(1+2+...+9)-(1/2+2/2+3/2+...+8/2)+(1/3+2/3+...+7/3)-...+1/9
=9(1+9)/2-(1+2+..+8)/2+(1+2+..+7)/3-..+1/9
=45-9*8/2/2+8*7/2/3-7*6/2/4+6*5/2/5-5*4/2/6+4*3/2/7-3*2/2/8+2*1/2/9
=45-18+28/3-21/4+3-5/3+6/7-3/8+1/9
=30-45/8+6/7+70/9
=