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Paragraph: Let f ( n ) denotes the number of different ways in which the positive integer n can be expressed as the sum of 1 's and 2 's. For example, f(4)=5 , since 4=2+2=2+1+1=1+2+1=1+1+2=1+1+1+1 . Note that order of 1 's and 2 's are important. Question: The value of f(6) is

Options

  1. A12
  2. B13
  3. C18
  4. D21

Correct answer

B. 13

Step-by-step solution

aligned & f(n)=2 f(n-1)-f(n-2)+f(n-4) n 5 . & Now f(1)=1, f(2)=2, f(3)=3, f(4)=5, f(5)=2 5-3+1=8, f(6)=2 8-5+2=13 aligned

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