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(A) To climb an $n$-step staircase,the person can reach the $n$-th step either from the $(n-1)$-th step (by taking one step) or from the $(n-2)$-th st

Vedclass · Accepted Answer

$C_{20}$

Vedclass · Answer

(A) To climb an $n$-step staircase,the person can reach the $n$-th step either from the $(n-1)$-th step (by taking one step) or from the $(n-2)$-th step (by taking two steps).Therefore,the recurrence relation is $C_n = C_{n-1} + C_{n-2}$ for $n \ge 2$.This is the definition of the Fibonacci sequence.Given the recurrence relation $C_n = C_{n-1} + C_{n-2}$,we can substitute $n = 20$ to get $C_{20} = C_{19} + C_{18}$.Thus,$C_{18} + C_{19} = C_{20}$.

$A$ person wants to climb a $n$-step staircase using one step or two steps at a time. Let $C_n$ denote the number of ways of climbing the $n$-step staircase. Then $C_{18} + C_{19}$ equals

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