计算：1−12+13−14+…+11997−11998+1199911+1999+12+2000+13+2001+…+1999+2997+11000+2998．

Question

计算：(1−(1)/(2)+(1)/(3)−(1)/(4)+…+(1)/(1997)−(1)/(1998)+(1)/(1999))/((1)/(1+1999)+(1)/(2+2000)+(1)/(3+2001)+…+(1)/(999+2997)+(1)/(1000+2998))．

Answer 1

分子=(1+(1)/(2)+(1)/(3)+(1)/(4)+…+(1)/(1997)+(1)/(1998)+(1)/(1999))−2×((1)/(2)+(1)/(4)+(1)/(6)+…+(1)/(1998))，
=(1+(1)/(2)+(1)/(3)+…+(1)/(1999))−(1+(1)/(2)+(1)/(3)+…+(1)/(999))，
=(1)/(1000)+(1)/(1001)+…+(1)/(1999)；
分母=(1)/(2000)+(1)/(2002)+(1)/(2004)+…+(1)/(3996)+(1)/(3998)
=2×((1)/(1000)+(1)/(1001)+…+(1)/(1999))；
原式=((1)/(1000)+(1)/(1001)+…+(1)/(1999))/(2×((1)/(1000)+(1)/(1001)+…+(1)/(1999)))＝(1)/(2)．