Question

三分之一+十五分之一+三十五分之一+六十三分之一+九十九分之一=？ 怎么简算急急急急急急急急急急急急急！

Answer 1

1/3+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)=1/3+1/2×1/3-1/2×1/11=1/2-1/2×1/11=1/2×10/11=5/11

中间的都消去了 这是一种方法

Answer 2

1/3+1/15+1/35+1/63+1/99
=1/3+1/3*5+1/5*7+1/7*9+1/9*11
=1/3+(1/3-1/5)/2+(1/5-1/7)/2+(1/7-1/9)/2+(1/9-1/11)2
=1/3+1/6-1/22
=1/2-1/22
=10/22=5/11

Answer 3

1/3+1/2(1/3-1/5)+1/2(1/5-1/7)+1/2(1/7-1/9)+1/2(1/9-1/11)=1/3+1/2×1/3-1/2×1/11=1/2-1/2×1/11=1/2×10/11=5/11