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Let f(n) denotes the number of different...

Let f(n) denotes the number of different ways, the positive integer n ca be expressed as the sum of the 1's and 2's. for example, f(4)=5.
i.e., `4=1+1+1+1`
`=1+1+2=1+2+1=2+1+1=2+2`
Q. The number of solutions of the equation `f(n)=n`, where `n in N` is

A

376

B

377

C

321

D

370

Text Solution

Verified by Experts

The correct Answer is:
B
`becausef(6)=.^(6)C_(0)+.^(5)C_(1)+.^(4)C_(2)+.^(3)C_(3)=13`
`thereforef{f(6)}=f(13)=.^(13)C_(0)+.^(12)C_(1)+.^(11)C_(2)+.^(10)C_(3)+.^(9)C_(4)+.^(8)C_(5)+.^(7)C_(6)`
`=1+12+55+120+126+56+7=377`.
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