PP1 PS-36 & PS-37有比較快的計算方法嗎

sangchangtw · 发表于 2009-10-4 17:48:00

#36
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards should be
(a) 3 and 15
(b) 3 and 20
(c) 4 and 13
(d) 4 and 14
(e) 5 and 14

不太了解這一題題目的意思說~(是只抽到一張數字(ex:5), 然後跟比這數字大的相乘,可是如果是這樣的我我怎麼知道他是乘上6還是...? 比5大的很多耶)

#37
For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1)^(k+1) x (1/2^k). If T is the sum of the terms in the sequence, then T is
(a) greater than 2
(b)between 1 and 2
(c)between 1/2 and 1
(d)between 1/4 and 1/2
(e)between 1/4..

我的算法是 (1-1/2)+(1/4-1/8)+(1/16-1/32)..+(1/2^9-1/2^10)
也是可以算
可是覺得好慢
請問有沒有比較快的算法呢

kepei7763 · 发表于 2009-10-4 20:30:00

第一题是不是选D啊？

就是说4*5=20 13*14=182

都没有超过15-20之间

Oia · 发表于 2009-10-4 21:42:00

#36 在于读懂题：一个人抽出一张牌，得到一个整数，然后乘以这个整数的下一个数，及n*(n+1)，结果在15-200之间。同意2楼的答案；

#37 就是估值问题：你括号中的每一项都>0，第一项是1/2，那么必然>1/2

如果将式子变更为：1-(1/2-1/4)-(1/8-1/16).....同样括号中的都大于0，那么必然<1

另外，也可以将这个数列看作是q=-1/2的等比数列，求和公式可以搞定。

dullness · 发表于 2009-10-5 12:34:00

#36
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards should be
(a) 3 and 15
(b) 3 and 20
(c) 4 and 13
(d) 4 and 14
(e) 5 and 14

不太了解這一題題目的意思說~(是只抽到一張數字(ex:5), 然後跟比這數字大的相乘,可是如果是這樣的我我怎麼知道他是乘上6還是...? 比5大的很多耶)

I vote C
3*4<15
4*5>15 least one:4

13*14<200 greatest one:13
14*15>200

#37
For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by (-1)^(k+1) x (1/2^k). If T is the sum of the terms in the sequence, then T is
(a) greater than 2
(b)between 1 and 2
(c)between 1/2 and 1
(d)between 1/4 and 1/2
(e)between 1/4..

1/2 -1/4 1/8 -1/16
sum is less than 1/2 （exclusive)
and greater than 1/4（exclusive)

yjz809 · 发表于 2009-10-5 13:02:00

agree with ls

PP1 PS-36 & PS-37有比較快的計算方法嗎

PP1 PS-36 & PS-37有比較快的計算方法嗎

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