(1)3/2+7/6+13/12+21/20+...111/110 (2)1-2+3-4+.-200+201

4个回答

  • (1) 3/2+7/6+13/12+21/20+...111/110

    =1+1/(1*2)+1+1/(2*3)+1+1/(3*4)+1+1/(4*5)+...+1+1/(10*11)

    =10+1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+...+1/(10*11)

    =10+(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/10-1/11)

    =10+1-1/11

    =10又(10/11)

    (2)1-2+3-4+.-200+201

    =(1-2)+(3-4)+...+(199-200)+201

    =-1*200/2 +201

    =-100+201

    =101