Question

小学巧算题及答案

1/2+1/6+1/12+1/20+1/30+...+1/9900

Answer 1

1/2+1/6+1/12+1/20+1/30+......+1/9900
=1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+......+1/99×100
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+......+1/99-1/100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+......+1/99-1/100
=1-1/100
=99/100

Answer 2

问题：1/2+1/6+1/12+1/20+1/30+...+1/9900

解：1-1/2+1/2-1/3+……+1/99-1/100=99/100

详细分析：
1/2+1/6+1/12+1/20+1/30+......+1/9900
=1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+......+1/99×100
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+（1/5-1/6）+......+1/99-1/100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+......+1/99-1/100
=1-1/100
=99/100

Answer 3

等于1-1/2+1/2-1/3+……+1/99-1/100=99/100