1.1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+...+49/50

1个回答

  • 1.1/2+1/3+2/3+1/4+2/4+3/4+1/5+2/5+3/5+4/5+...+49/50=1/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+...+49/50=1/2+2/2+3/2+4/2+5/2+...+49/2=1/2(1+2+3+4+5+...+49)=1225/2=612又1/2

    2.19+9又1/2+7又1/4+3又1/8+8又1/16+4又1/32

    =19+9+1/2+7+1/4+3+1/8+8+1/16+4+1/32

    =19+9+7+3+8+4+1/2+1/4+1/8+1/16+1/32

    =50+31/32=50又31/32

    3.(1+1/2+1/3+1/4)*(1/2+1/3+1/4+1/5)-(1+1/2+1/3+1/4+1/5)*(1/2+1/3*1/4)

    设)(1/2+1/3*1/4)=x,原式= (1+x)*(x+1/5)-(1+x+1/5)*x=1/5