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Quarrippesspevmo

Quarrippesspevmo

Answered question

2022-06-01

Consider the sequence
a n = n 2 3 n + 3 2 n n
With a string of inequalities, one can show that a n is bounded and the graph of the function f ( x ) = x 2 3 x + 3 2 x x suggests that f is monotone, but how could one prove convergence and a calculate the limit of a n ?

Answer & Explanation

polomierzvxe4b

polomierzvxe4b

Beginner2022-06-02Added 3 answers

Rewrite as lim 8 1 + ( 9 / 8 ) n n lim 8 ( 9 / 8 ) n n = 9 and
lim 8 n + ( 9 / 8 ) n n lim 8 2 ( 9 / 8 ) n n = 9.
So the limit is 9

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