For each positive integer n, let `A_n=max{(C(n,r) 0 le r le n}` then the number of elements n in {1,2...20} for `1.9 le (A_n)/(A_(n-1)) le 2` is

Options

A. 9
B. 10
C. 11
D. 12

Answer

C

Explanation

Case (1) n=even
`(A_(n))/(A_(n-1))=(.^(n)C_(n//2))/(C_((n-1-1)/(2)))=2`
so for all n even given relation is true
Case (2) n=odd
`(A_(n))/(A_(n-1))=(.^(n)C_((n-1)/2))/(.^(n-1)C_((n-1)/(2)))=(2n)/(n+1)`
which satisfies only for n=19