You can use sigma notation to simplify the title function.
I've forgotten my math...
Is there an easier way to express the function in my title? Here's the context:
In Simcity you can buy a coal plant for $10000. Every year you own it it costs $1 per month * number of years owned * 12 months to maintain. If I've owned the plant for 20 years, it costed me $240 that year, $228 the previous year, $216 the year before that, etc. If I buy a new plant, the maintenance costs go back down to $12 for the year again. So what's the most affordable way to keep using coal plants?
I was thinking, let x = number of years between buying a new plant, and then I could come up with a function that tells me what the cost would be for every x years. It would be something like 10,000 + 12x + 12(x-1) + 12(x-2) and so on, but that's not so easy to evaluate for larger numbers.
So is there a way to simplify that expression? (Or should I just go wind power)?
Thanks in advance!
2. If so I'm going to modify your notation a little bit:
3. The sum of the first n natural numbers is calculated by:
4. Thus your sum becomes: