初中数学

显示全部楼层 · 2005-10-17 21:03:38

(1/2) + (1/3 + 2/3) + (? + 2/4 + 3/4) + .... )+ … + (1/50 + 2/50 + … + 49/50)= (1/2) + (1 + 2)/3 + (1 + 2 + 3)/4 + ... + (1 + 2 + 3 + ... +49)/50= (1/2)+ [(1 + 2)*2/2]/3 .... 1 + 2 = 3+ [(1 + 3)*3/2]/4 .... 1 + 3 = 4+ [(1 + 4)*4/2]/5 .... 1 + 4 = 5+ ...+ [(1 + 49)*49/2]/50 ..1 + 49 = 50= (1/2)+ 2/2+ 3/2+ 4/2+ ...+ 49/2= (1 + 2 + 3 + ... + 49)/2= [(1 + 49)*49/2]/2= 25/98

千问 · 2005-10-17 21:03:38

原式=0.5+1+1.5+2+......+0.5*49
=0.5(1+2+3+......+49)
=0.5*49/2
=49/4

千问 · 2005-10-17 21:03:38

An=1/(n+1)+2/(n+1)+3/(n+1)+…+n/(n+1)=(1+2+3+…+n)/(n+1)=n(n+1)/2(n+1)=n/21/2+(1/3+2/3)+(1/4+2/4+3/4)+(1/5+2/5+3/5+4/5)+…+(1/50+2/50+…+49/50)=A1+A2+A3+…+A49=(1+2+3+…+49)/2=49×50÷4=612.5用此方法不只可以算到第49项，你可以试试算到100项等

千问 · 2005-10-17 21:03:38

解原式=0.5+1+1.5+2+……+24.5+25=(25+0.5)×(25×2÷2)=637.5