(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

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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 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,$C_{18} + C_{19} = C_{20}$.

Class 11 Mathematics Sequences and Series nth term of special series, Sum to n terms and Infinite number of terms

$A$ 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

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

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Sequences and Series

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nth term of special series, Sum to n terms and Infinite number of terms

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Medium

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DifficultJEE MAIN 2023

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If $\alpha \in R, n \in N$ and $n+2(n-1)+3(n-2)+\ldots+(n-1)2+n.1 = \alpha n(n+1)(n+2)$,then $\alpha =$

MediumTS EAMCET 2019

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The sum of an infinite number of terms in a $G.P.$ is $20$ and the sum of their squares is $100$. The common ratio of the $G.P.$ is:

MediumAIEEE 2002

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$A$ 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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