Re: [計量] 請教兩題計量
※ 引述《bluecocoa (擁抱大白熊 )》之銘言：
if 1 < n < 5, n is an interger
請問 the sum of the first n odd integers that are greater than zero
和 n^2-1 何者為大？
這題我連題目都看不太懂 囧
1 < n < 5, n is an interger
=> n=2,3,4
let S(n)=the sum of the first n odd integers that are greater than zero
L(n)=n^2-1
n=2
S(2)=1+3=4
L(2)=4-1=3
n=3
S(3)=1+3+5=9
L(3)=9-1=8
n=4
S(4)=1+3+5+7=16
L(4)=16-1=15
That is S(n)=1+3+5+7+...+(2*n-1)
S(n)={[(2*n-1)+1]*n}/2= n^2
So S(n)=n^2 > n^2 -1 = L(n)
還有
A positive integer with exactly two different divisors greater than 1 must be
a) a prime 我想到的反例為2*3＝6
b) an even integer 反例為3*5＝15
c) a multiple of 3 反例同上
d) the square of a prime
e) the square of an odd interger
選項d和e我都不是很懂
可以請大家教教我嗎？
謝謝！
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