Determine Whether The Given Sequence Is...

iJoe

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Determine whether the given sequence is increasing,decreasing, or not monotonic. an = ( 3n + 4 ) / ( 2n + 5 )

 

Answer No.1

Anonymous

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D/dn(an)=((2n+5)(3)-(3n+4)(2))/(2n+5)^2 =7/(2n+5)^2>0, so the sequence is always increasing.

Answer No.2

Anonymous

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Let f(n) = 3n+4 / 2n+5 if f '(n) > 0 then the sequence is increasing if f '(n) < 0 then the sequence is decreasing if f '(n) = 0 then you'll need to find second derivative toconclude. f '(n) = 3(2n+5)-(3n+4)(2) / (2n+5)^2 = 7 / (2n+5)^2> 0 for all n. Thus f '(n) > 0 and the sequence is increasing.

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