(A) To climb a staircase of $n$ steps,the person can either take a single step from the $(n-1)$-th step or a double step from the $(n-2)$-th step.This

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(A) To climb a staircase of $n$ steps,the person can either take a single step from the $(n-1)$-th step or a double step from the $(n-2)$-th step.This gives the recurrence relation: $C_n = C_{n-1} + C_{n-2}$ for $n > 2$.This is the definition of the Fibonacci sequence.Given the relation $C_n = C_{n-1} + C_{n-2}$,we can substitute $n = 20$ into the formula.Thus,$C_{20} = C_{19} + C_{18}$.Therefore,$C_{18} + C_{19} = C_{20}$.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

Medium

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

A
$C_{20}$
B
$C_{21}$
C
greater than $C_{21}$
D
less than $C_{20}$

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

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