6. 26-1=25（场）
答：一共要进行25场比赛才能产生冠军

7. (4+10)x11÷2=77（根）
答：这堆圆木共有77根

1/1x2+1/2x3+1/3x4+...+1/9x10
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10
=1-1/10
=9/10

1/1x2-1/2x3-1/3x4-...-1/9x8
=1-1/2-1/2+1/3-1/3+1/4-...-1/8+1/9
=1-1+1/9
=1/9

2/1x3+2/3x5+2/5x7+...+2/97x99
=1-(1/3)+(1/3)-(1/5)+(1/5)-(1/7)+……+(1/97)-(1/99)
=1-(1/99)
=98/99

6. 26-1=25（场）
答：一共要进行25场比赛才能产生冠军

7. (4+10)x11÷2=77（根）
答：这堆圆木共有77根

1/1x2+1/2x3+1/3x4+...+1/9x10
=1-1/2+1/2-1/3+1/3-1/4+...+1/9-1/10
=1-1/10
=9/10

1/1x2-1/2x3-1/3x4-...-1/9x8
=1-1/2-1/2+1/3-1/3+1/4-...-1/8+1/9
=1-1+1/9
=1/9

2/1x3+2/3x5+2/5x7+...+2/97x99
=1-(1/3)+(1/3)-(1/5)+(1/5)-(1/7)+……+(1/97)-(1/99)
=1-(1/99)
=98/99