Prep数学请教

xiaolingdang

In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and kate's annual salaries. If Mary's annual salary was the highest of 3 people, what was the average (arithmetic mean) annual salary of the three people.

答案好像是：只要知道kate's salary 就可以解这题。。。为啥么呀？我选的是要知道两个人的annual salary那个选项。。

 

再问一下：1/2-1/2^2+1/2^3+....-1/2^10是什么范围怎么变形计算的哦？答案是：between1/4 and 1/2.

谢谢啦：） 

taoyeye

1.M-J=2(M-K), M-J-2M+2K=0, 2K=J+M, (K+M+J)/3=(K+2K)/3=K,所以知道Kate's salary 就可以了。

 

carollai

 2.等比数列求和，等比为（-1/2),项数为10.公式：Sn=a1(1-q^n)/(1-q) =(a1+an*q)/(1-q)

原式=1/3(1-1/2^10)

可能还有其他更简单的方法吧~

xiaolingdang

 恩，谢谢，都明白啦；）