help please? Consider the veracity or falsehood of each of the following stateme

Question

help please?

Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false. We let Fn stand for the nth Fibonacci number. If n is a multiple of 3 then Fn is a multiple of 4. Fn is a multiple of 9 if and only if Fn is a multiple of 6. If Fn is a multiple of 5, then n is a multiple of 5. If Fn is a multiple of 9, then n is a multiple of 24. For any positive real number x, x + 1/x 2.

Explanation / Answer

1)False ,for n=3, Fn =2 not a multiple of 4...

2) True,

3)True, We know for a fibonacci seqn Fkn is divible by Fn..

hence F5k will be divisible by F5=5

hence for all n= 5k , Fn is a multiple of 5..

4) False, F12= 144 multiple of 9 , but n=12 not a multiple of 24

5) True ...for any positive no x ,

AM>=GM

=> (x+1/x)/2 > sqrt (x*1/x)

=>x+1/x > 2
Proved

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