THE STAIRCASE PROBLEM Our challenge is to find out how many ways you can climb a staircase with n mmbers of stairs. You have fairly long legs, which allow you option of taking the steps either one or two at a time. You can also use any combination of one and two steps for longer staircase. Let's get started For a staircase with only one step there is only one way of climbing it You take one step to the top. If there were two steps you could take one step at a time or you could take both steps in one stride Now let's consider different length staircase. Can you fill in the table below with the mmber of possible ways of climbing each staircase and come up with a formula for a stair case of any length? Number 1 2 3 10 N of Steps Number of Ways Explain your sequence in words.
THE STAIRCASE PROBLEM Our challenge is to find out how many ways you can climb a staircase with n mmbers of stairs. You have fairly long legs, which allow you option of taking the steps either one or two at a time. You can also use any combination of one and two steps for longer staircase. Let's get started For a staircase with only one step there is only one way of climbing it You take one step to the top. If there were two steps you could take one step at a time or you could take both steps in one stride Now let's consider different length staircase. Can you fill in the table below with the mmber of possible ways of climbing each staircase and come up with a formula for a stair case of any length? Number 1 2 3 10 N of Steps Number of Ways Explain your sequence in words.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:THE STAIRCASE PROBLEM
Our challenge is to find out how many ways you can climb a staircase with n mmbers of stairs.
You have fairly long legs, which allow you option of taking the steps either one or two at a time. You
can also use any combination of one and two steps for longer staircase.
Let's get started For a staircase with only one step there is only one way of climbing it. You take one
step to the top. If there were two steps you could take one step at a time or you could take both steps in
one stride.
Now let's consider different length staircase. Can you fill in the table below with the mmber of possible
ways of cimbing each staircase and come up with a formula for a staircase of any length?
Number
1
2
3
4
10
N
of Steps
Number
of Ways
Explain your sequence in words.
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