苹果焕新计划：4年均付7-8折 iPhone Upgrade Program: Every Year, a Latest iPhone with 20%-30% Discount

Suppose, every year, you buy a new iPhone at 8388 yuan RMB plus Apple Care+ for 1688 yuan RMB.
First, calculate the extra money you have to pay every year.
Add the AC cost for the previous year, subtract half of the AC returned by Apple, add the extra money you have to pay with half of the originals price of the old phone. The number is 1688-844+8388/2=5044
Every year, for a new iPhone, you have to pay f(n)=（8388+5044n)/(1+n). n-->+oo, f(n)=5044
For n=1,2,3, the price is 6716,6158, 5880. n-->+oo, f(n)=5044
The discount is 20%-30%

Suppose, this year, you buy a new iPhone at 8388 yuan RMB plus Apple Care+ for 1688 yuan RMB. From the second year, you choose to buy a new iPhone at 5388 yuan with Apple Care+ for 988 yuan RMB.
First calculate the extra money you have to pay every year.
The process is a little complicated , but similar to the one in the first scenario. The result is 3438
Every year, for a new iPhone, you have to pay f(n)=（10920+3438n)/(1+n). n-->+oo, f(n)=3488
For n=1,2,3, the price is 5460, 4802,4461
The discount is around 30%

Suppose, you buy a new iPhone at a price from 5888 to 8388 plus AC, the discount is 20%-30%, between the two extreme above.

苹果焕新计划：连续买4年，年均支付新机价格7-8折

今年苹果发布了两款最新手机，iPhoneX(基础款8388元） iPhone8（(基础款5888元）明年是否还发布8388元手机和5888元两款手机？还是只发布某一款，如5388元？这里分两个表格，第一个是消费者连续每年买最高价位手机（例如今年最高的是8388元）和AC（目前的8388元的AC是1688元）；第二个消费者以后每年买5888元和相应的AC（目前为988元）。

计算的是连续买n年，前n年每个手机平均支付多少，折合零售价格的几折？

好像这里无法粘贴表格，烦劳点击这个公共号文章吧。

苹果焕新计划：连续买4年，年均支付新机价格7-8折 https://mp.weixin.qq.com/s/GomXl1WyQ9L0fGH415AvZw

对于第一个表格就是

连续购买n年，每年平均支付 f(n)=（8388+5044n)/(1+n) ，当n趋近无穷大时，f(n)无限趋近5044元。假定最新机器永远8388，那么折扣无限趋近 6折。购买的年数越少，折扣越少。

对于第二个表格就是

从2019年起需要额外支付的费用：上年AC费用 988/2+（5888-5888/2）=3438元

连续购买n年，每年平均支付 f(n)=（10920+3438n)/(1+n) 极限，无限趋近3438元，如果最新手机固定在5888，折扣逼近0.58折。