With each step you take when climbing a staircase, you can move up either one stair or two stairs. As a result, you can climb the entire staircase taking one climb the entire staircase takimg one stair at a time, taking two at a time, or taking a combination of one-and two-stair increments. For each integer n ≥ 1 , if the staircase consist of n stairs, let c n be the number of different ways to climb the straircae. Find a recurrenvce relation c 1 , c 2 , c 3 , .... Justify your answer.
With each step you take when climbing a staircase, you can move up either one stair or two stairs. As a result, you can climb the entire staircase taking one climb the entire staircase takimg one stair at a time, taking two at a time, or taking a combination of one-and two-stair increments. For each integer n ≥ 1 , if the staircase consist of n stairs, let c n be the number of different ways to climb the straircae. Find a recurrenvce relation c 1 , c 2 , c 3 , .... Justify your answer.
Solution Summary: The author calculates a recurrence relation for each integer nge 1.
With each step you take when climbing a staircase, you can move up either one stair or two stairs. As a result, you can climb the entire staircase taking one climb the entire staircase takimg one stair at a time, taking two at a time, or taking a combination of one-and two-stair increments. For each integer
n
≥
1
, if the staircase consist of n stairs, let
c
n
be the number of different ways to climb the straircae. Find a recurrenvce relation
c
1
,
c
2
,
c
3
,
....
Justify your answer.
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