差異處
這裏顯示兩個版本的差異處。
| 兩邊的前次修訂版 前次修改 | |||
| start:math:20121120 [2012/11/24 16:41] – jonathan | start:math:20121120 [2019/10/08 14:09] (目前版本) – jonathan_tsai | ||
|---|---|---|---|
| 行 1: | 行 1: | ||
| + | ====== 正方形數(平方數) ====== | ||
| + | |||
| + | < | ||
| + | 1 + 3 + 5 + 7 + ___ = ? | ||
| + | </ | ||
| + | |||
| + | * 答案: 總數 = 25 , 最後一個數 = 9 | ||
| + | * 算法: 5*5 = 25 , 5+5-1 = 9 | ||
| + | * 為何這樣算? | ||
| + | < | ||
| + | 1 => x | ||
| + | 3 => 0x | ||
| + | xx | ||
| + | 5 => 00x | ||
| + | 00x | ||
| + | xxx | ||
| + | 7 => 000x | ||
| + | 000x | ||
| + | 000x | ||
| + | xxxx | ||
| + | 9 => 0000x | ||
| + | 0000x | ||
| + | 0000x | ||
| + | 0000x | ||
| + | xxxxx | ||
| + | </ | ||
| + | * 所以當出現數列有 5 個, 那總和就是 5*5=25 , 最後一個數是 5+5-1＝9 (扣掉右下角重複計算的數) | ||
| + | * 因此可以推出公式 => 總和=n*n 最後一個數=n+n-1 | ||
| + | |||
| + | |||
| + | < | ||
| + | 1 + 3 + 5 + .... + ___ = ? (數列有 90 個) | ||
| + | </ | ||
| + | * Sum = 90*90=8100 | ||
| + | * Last = 90+90-1=179 | ||
| + | |||
| + | < | ||
| + | 37 + 39 + 41 + 43 + .... + ___ = ? (數列有 90 個) | ||
| + | </ | ||
| + | * 看成兩個正方形數列 | ||
| + | * 1 + 3 + ... + 35 (數列有 n+n-1=35 => n=18 個) | ||
| + | * 1 + 3 + ... + __ (數列有 18 + 90 = 108 個) | ||
| + | * Sum = 108*108 - 18*18 = 11664-324=11340 | ||
| + | * Last = 108+108-1 = 215 | ||