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发表于 2020-2-9 01:57:34 | 显示全部楼层 |阅读模式

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毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-2-9 11:49:53 | 显示全部楼层
先从简单想起。

1+2+3+4+5+6+7+8+9+10+11+12+13
=1×2/2+2×2/2+3×2/2+4×2/2+5×2/2
=(1×2/2+2×2/2)+3×2/2+4×2/2+5×2/2
=(2×3)/2+3×4/2+4×2/2+5×2/2
=(2×3/2+3×2/2)+4×2/2+5×2/2
=(3×4)/2+4×2/2+5×2/2
=(3×4/2+4×2/2)+5×2/2
=(4×5)/2+5×2/2+6×2/2
=(4×5/2+5×2/2)+6×2/2
=(5×6)/2+6×2/2+7×2/2
=(5×6/2+6×2/2)+7×2/2
=(6×7)/2+7×2/2+8×2/2
=(6×7/2+7×2/2)+8×2/2
=(7×8)/2+8×2/2+9×2/2

1×2+2×3+3×4+4×5+5×6+6×7+7×8+8×9
=1×2×3/3+2×3×3/3+3×4×3/3+4×5×3/3
=(1×2×3/3+2×3×3/3)+3×4×3/3+4×5×3/3
=(2×3×4)/3+3×4×3/3+4×5×3/3+5×6×3/3
=(2×3×4/3+3×4×3/3)+4×5×3/3+5×6×3/3
=(3×4×5)/3+4×5×3/3+5×6×3/3
=(3×4×5/3+4×5×3/3)+5×6×3/3
=(4×5×6)/3+5×6×3/3+6×7×3/3
=(4×5×6/3+5×6×3/3)+6×7×3/3
=(5×6×7)/3+6×7×3/3+7×8×3/3
=(5×6×7/3+6×7×3/3)+7×8×3/3
=(6×7×8)/3+7×8×3/3+8×9×3/3

1×2×3+2×3×4+3×4×5+4×5×6+5×6×7+6×7×8+7×8×9
=1×2×3×4/4+2×3×4×4/4+3×4×5×4/4+4×5×6×4/4
=(1×2×3×4/4+2×3×4×4/4)+3×4×5×4/4+4×5×6×4/4
=(2×3×4×5)/4+3×4×5×4/4+4×5×6×4/4+5×6×7×4/4
=(2×3×4×5/4+3×4×5×4/4)+4×5×6×4/4+5×6×7×4/4
=(3×4×5×6)/4+4×5×6×4/4+5×6×7×4/4
=(3×4×5×6/4+4×5×6×4/4)+5×6×7×4/4
=(4×5×6×7)/4+5×6×7×4/4+6×7×8×4/4
=(4×5×6×7/4+5×6×7×4/4)+6×7×8×4/4
=(5×6×7×8)/4+6×7×8×4/4+7×8×9×4/4

1×2×3×4+2×3×4×5+3×4×5×6+4×5×6×7+5×6×7×8+6×7×8×9
=1×2×3×4×5/5+2×3×4×5×5/5+3×4×5×6×5/5+4×5×6×7×5/5
=(1×2×3×4×5/5+2×3×4×5×5/5)+3×4×5×6×5/5+4×5×6×7×5/5
=(2×3×4×5×6)/5+3×4×5×6×5/5+4×5×6×7×5/5+5×6×7×8×5/5
=(2×3×4×5×6/5+3×4×5×6×5/5)+4×5×6×7×5/5+5×6×7×8×5/5
=(3×4×5×6×7)/5+4×5×6×7×5/5+5×6×7×8×5/5
=(3×4×5×6×7/5+4×5×6×7×5/5)+5×6×7×8×5/5
=(4×5×6×7×8)/5+5×6×7×8×5/5+6×7×8×9×5/5
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-2-9 12:39:04 | 显示全部楼层
screen02.png
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
 楼主| 发表于 2020-2-9 13:03:48 | 显示全部楼层
screen03.png
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-2-9 13:54:11 | 显示全部楼层
我只会玩这些简单的。
1^2=1+0×1
2^2=2+1×2
3^2=3+2×3
4^2=4+3×4
5^2=5+4×5
6^2=6+5×6
7^2=7+6×7
8^2=8+7×8
9^2=9+8×9
............
\(\D\sum_{i=1}^n n^2=\frac{n(n+1)}{2}+\frac{(n-1)n(n+1)}{3}=\frac{n(n+1)(2n+1)}{6}\)
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-2-10 18:32:33 | 显示全部楼层
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
发表于 2020-2-11 21:04:00 | 显示全部楼层
毋因群疑而阻独见  毋任己意而废人言
毋私小惠而伤大体  毋借公论以快私情
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