Question

let be the number of ways to climb stairs if a person climbing the stairs can take one stair or two stairs at a time. identify the recurrence relation that represents :

Answer 1

The recurrence relation for the number of ways to climb stairs taking one or two steps at a time is T(n) = T(n-1) + T(n-2), resembling the Fibonacci sequence.

Step-by-step explanation:

The student has asked to identify the recurrence relation that represents the number of ways to climb stairs if a person can take one stair or two stairs at a time. Let's denote this number of ways as T(n), where n is the total number of stairs. The recurrence relation can be written as T(n) = T(n-1) + T(n-2), with the initial conditions T(1) = 1 and T(2) = 2. This means that the ways to climb to the nth stair depends on the ways to climb to the (n-1)th stair plus the ways to climb to the (n-2)th stair.

To explain further, a person can either reach the nth stair from the (n-1)th stair with a single step or from the (n-2)th stair with a double step. This is a classic example of a Fibonacci sequence, where each number is the sum of the two preceding ones, starting from 0 and 1.