除左用計數機外, 有無D快D既方法去計??
Q1) 1+2+3+...+42 =??
Q2) 1+2+3+...+18+19+18+...+3+2+1= ??
Q3) 1+3+5+...+67= ??
P.6 數學題
2007-06-13 11:59 pm
回答 (2)
2007-06-14 12:06 am
✔ 最佳答案
1+2+3+...+n = (1+n)(n)/2 [(首項+末項)*項數/2]Q1) 1+2+3+...+42 =??
=(1+42)(42)/2
=43(21)
= 903
Q2) 1+2+3+...+18+19+18+. ..+3+2+1= ??
=(1+18)(18)/2 *2 +19
=19(18) +19
=361
Q3) 1+3+5+...+67= ??
=(1+67)(34)/2
=68(17)
=1156
2007-06-14 12:16 am
1) 1+2+3+...+42
= 42 X (42+1) / 2
= 903
2) 1+2+3+...+18+19+18+...+3+2+1
= 2 X (1+2+3+...+18) + 19
= 2 X (18 X (18+1) / 2) + 19
= (18 X 19) +19
= 342 + 19
= 361
3) 1+3+5+...+67
= 1 + (2+1) + (3+2) + ... + (33+32) + (34+33)
= 2 X (1+2+3+...+33) + 34
= 2 X (33 X (33+1) / 2) +34
= (33 X 34) + 34
= 1122 + 34
= 1156
= 42 X (42+1) / 2
= 903
2) 1+2+3+...+18+19+18+...+3+2+1
= 2 X (1+2+3+...+18) + 19
= 2 X (18 X (18+1) / 2) + 19
= (18 X 19) +19
= 342 + 19
= 361
3) 1+3+5+...+67
= 1 + (2+1) + (3+2) + ... + (33+32) + (34+33)
= 2 X (1+2+3+...+33) + 34
= 2 X (33 X (33+1) / 2) +34
= (33 X 34) + 34
= 1122 + 34
= 1156
參考: ME
收錄日期: 2021-04-13 00:56:59
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