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Consider the following problem: We have the following sets:

A={S where S is a bounded sequence of natural numbers}
B={S where S is an increasing bounded sequence of natural numbers}

I need to...

Yes indeed, my mistake for not clarifying this. When n=2 there are 4 cards, 2 yellow and 2 green, and when n=3 there are 6 cards, 3 yellow and 3 green. And whne purchasing you get one card. :)

In a coupon collecting game there are two different kinds of coupons, the green and the yellow ones. Each kind has n different coupons. We want to gather only one kind: either all the green ones or...

It is okay, I've found it! Thank you for your immediate reply! You can indeed solve it by induction. For n = 0, it's true, since 8/3 < 4. Let's suppose it holds true for n=k. Then we have to show...

Consider the set S which is defined as:

1. (1,1) belongs to S
2. if (x,y) belongs to S, then (y,x) belongs to S
3. if (x,y) belongs to S, then (x,x+2y) belongs to S.

What set is S?

Help:...

I need to prove by induction that for every n => 0,
8/1*3 + 8/5*7 +... + 8/(4n+1)*(4n+3) <= 4

Every help is welcome!