NN们帮忙看两道Prep的题

waytousff

IF $1000 is deposited in a bank account and remains in the account along with accumulated interest, the dollar amount of interest, I = 1000* ((1+r/100)^n-1), where r percent is the annual interest rate paid by the bank. Is the annual interest rate paid by the bank greater than 8 percent?
(1) the deposit earns a total of $210 in interest in the first two years.
(2) (1+r/100)^2 > 1.15
答案是A
我不明白的是(2)不是明明可以算出来吗.为什么答案不可以.
2. For every positive even integer n, the function h(n) is defined to be the product of all the even integers from 2 to n, inclusive. If p is the smallest prime factor of h(100) + 1, then p is
A between 2 and 10
B between 10 and 20
...
E greater than 40
答案是E,
不太明白怎么做,花了好几分钟.
谢谢!

windyYe

此答案不好。从其他地方搜出的答案如下：

首先由题知，h(n)=2x4x6x8x......xn
将n=100代入h(n)得，h(100)=2x4x6x8x......x98x100
然后可以将每一项变形，比如2变成1x2，4变成2x2，6变成3x2，8变成4x2，由此可得
h(100)=1x2x2x2x3x2x4x2x...48x2x49x2x50x2
再变形得h(100)=2^50x50! ∴h(100)+1=2^50x50!+1
h(100)=2^50x50!可以被任何大于等于2小于等于50的integer整除。
∴h(100)+1=2^50x50!+1被任何大于等于2小于等于50的integer n除，结果必是一个整数加上(1/n)的形式，也就是h(100)+1无法被between 2 and 50的任何整数整除。所以就只能选答案E了

waytousff

谢谢楼上的解答.

1题当成等号了,没有算,以为一定能算出来,所以可以判断大小.

HenriWilligS

关于第一题，I = 1000* ((1+r/100)^n-1)是不是抄错题目了？

zhanghaolin

# h(100)的prime factor为从2，3，5，7，11，。。到47。

所以h(100)+1必然不能被2,3,....47之中任意一个prime整除

所以h(100)+1的smallest prime factor必然大于47         所以选 E

jingjane

我来试试吧

第一个题 2算出来R>7点几 无法证明R>8

第二题 2*4*6*....*100+1 前一项的PRIME FACTOR有3,5,7....41,43,47 因为加上1 所以这个PRIME FACTOR应该大于47