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I've got a sequence defined as such:

  • between 0 and 5, $i = 1$
  • between 6 and 10, $i = 1*d$
  • between 11 and 15, $i = 1*d^2$
  • between 16 and 20, $i = 1*d^3$
  • ...

I guess I could write it like this for n=5:

between $k(n)+1$ and $(k+1)n$, $i= 1*d^k$

and I'm looking for the nth term of the induced serie. (ie the sum of the Nth first terms of my sequence)

Actually, I'm trying to solve a real-world problem here. We're selling products with a progressive discount (eg the first 5 items are at full price, then the 5 following items have a 10% discount, then there's an extra 10 percent discount for the next clip of 5, etc).

So far I'm handling this kind of manually (basically, I've created a table with all the possible values up to 1000 - we're not selling Lamborghini's, but still we don't expect a single customer to buy more than 1000 item from us, ever), and I'm quite curious to know how one would solve this using a single math formula.

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    Quite a discount! If the regular price of an item is $100$ dollars, then when you get to around three hundred items, the last five are about $2$ cents each, an interesting instance of the magic of compounding. On a more serious note, you could generate a formula for determining *total cost* if $n$ items are bought instead of unit prices. It is a small variant of summing a (finite) geometric series.2011-07-17

2 Answers 2