(1) 原式=(5-1)*(1+5+5^2+5^3+…+5^n)/(5-1)-1=(5^(n+1)-1)/4-1 (2)1/2+(1/4+3/4)+(1/6+3/6+5/6)……+(1/98+3/98+……+97/98) =1/2+1+3/2+2+5/2+...+49/2 =(1/2)*(1+2+3+...+49) =(1/2)*(1+49)*49/2 =1225/2. (3)1-1/1*2-2/(1+1)*(1+2)-3/(1+2)*(1+2+3)(1+2+3)-4/(1+2+3)*(1+2+3+4)-.-10/(1+2+3+4+5+6+7+8+9)*(1+2+3+4+5+6+7+8+9+10) =1-(1-1/2)-[1/(1+1)-1/(1+2)]-[1/(1+2)-1/(1+2+3)]-.-[1/(1+2+3+4+5+6+7+8+9)-1/(1+2+3+4+5+6+7+8+9+10)] =1-1+1/2-1/(1+1)+1/(1+2)-(1+2)+1/(1+2+3)-1/(1+2+3)+1/(1+2+3)-.-1/(1+2+3+4+5+6+7+8)+1/(1+2+3+4+5+6+7+8+9)-1/(1+2+3+4+5+6+7+8+9)+1/(1+2+3+4+5+6+7+8+9+10) =1/(1+2+3+4+5+6+7+8+9+10) =1/55 (4)1/2001+2/2001+3/2001+4/2001+``````````+1999/2001+2001/2001=(1+2+3+4+……+2001)/2001=[(1+2000)*2000/2+2001]/2001=1001*2001/2001=1001 (5)原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/n-1/(n+1) =1-1/(n+1)=n/(n+1)〉1921/2001,用1同时减去两边 推出:1/(n+1)