Suppose you have x amount of bagels, each day you must eat 1 bagel minimum or 2 bagels maximum..how many different ways can you eat all the bagels?
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2We assume that all bagels are identical. For comfort we use $n$ rather than $x$. Let $a_n$ be the number of ways. Argue that for $n\ge 2$, $a_n=a_{n-1}+a_{n-2}$. – André Nicolas Apr 07 '15 at 21:24
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Note that this is essentially the same as this problem. – Brian M. Scott Apr 07 '15 at 21:29