2.還原法
1和1/1+3和2/1+5和3/11+7和4/11+...
=1+1/11+3+2/11+5+3/11+7+4/11+......+19+10/11
=(1+3+5+7+......+19)+(1/11+2/11+3/11+4/11+......+10/11)
=(1+19)*10/2+(1/11+10/11)*10/2
=100+5
=105
3.分裂術語法
1/2*3+1/3*4+1/4*5.....+1/99*100
1/2*3+1/3*4+1/4*5.....+1/99*100
=1/2-1/3+1/3-1/4+……+1/99-1/100
=1/2-1/100
=49/100
1/1*2*3+1/2*3*4+......+1/98*99*100
= (1/ 1 * 2-1/1 * 3)+(1/2 * 3-1/2 * 4)+...n(n+1)-1/n(n+2)，1/n(n+1)-1/n(n+2)= n+2-(n-66)的形式。)
= (1/1 * 2+1/2 * 3+1/3 * 4+...+1/98 * 99)-(1/65438+)
= (1/1-1/2+1/3+1/3-1/4+...1/.
= (1/1-1/99)-1/2 (1/1/3+1/2-65438+
= 98/99-1/2(1/1/2-1/99-1/100)(這裏註意消去後剩下的是4。