If f is the function defined for all k by f(k) = k^5/16,what is f(2k) in terms of f(k)?

题目

If f is the function defined for all k by f(k) = k^5/16,what is f(2k) in terms of f(k)?
A.1/8 f(k)
B.5/8 f(k)
C.2 f(k)
D.10 f(k)
E.32 f(k)
标答是D,但我怎么求都是E
另外一道,If an integer n is to be chosen at random from the integers 1 to 96,inclusive,what is the probability that n(n + 1)(n + 2) will be divisible by
A.1/4
B.3/8
C.1/2
D.5/8
E.3/4
标答是D,我可以求出3/8,但是这样就不包含2、4等正解,所以求正确的解法有木有啊!

答案

第一题答案显然是E.第二题,首先若n是偶数的话,这个数一定是被8整除的.证明：令n=2k,k为整数.n(n + 1)(n + 2)=2k(2k+1)(2k+2)= 4k(k+1)(2k+1),而这里,k(k+1)必为一奇一偶,所以还藏着一个因子2.此外,n为奇数的时候,令n...