Question

A) find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one, two,

Answer 1

Answer:

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Answer 2

Let A n be the number of ways to climb the n stairs. In order to climb n stairs, a person must either start with a step on one stairs and then climb n - 1 stairs ( and this can be done in A n - 1 ways) or else start with the step of two stairs and then climb n - 2stairs (and this can be done in A n -2ways).

From this analysis we can immediately write down the recurrence relation, valid for all n _>2:a n = a n - 1+ a n - 2

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