a_1 =(1/2). a_n =(2/(n+3))+(1−(1/(n+3)))^2 a_(n−1) . Find the maximum of a


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Question Number 219408 by CrispyXYZ last updated on 24/Apr/25

$a_{1} = \frac{1}{2} . a_{n} = \frac{2}{n + 3} + {(1 - \frac{1}{n + 3})}^{2} a_{n - 1} .$ $Find the maximum of a_{n} .$
	Answered by SdC355 last updated on 24/Apr/25

	$a_{n} = \frac{c_{1} + n (n + 7) + 12}{{(n + 3)}^{2}}$ $a_{1} = \frac{c_{1} + 20}{16} = \frac{1}{2} c_{1} = - 12$ $a_{n} = \frac{n (n + 7)}{{(n + 3)}^{2}}, n = 21 \max a_{n} = \frac{49}{48}$
	Commented by universe last updated on 24/Apr/25

	$s i r c a n y o u e x p l a i n h o w t o f i n d y o u v a l u e o f$ $a_{n} ? ?$
	Answered by universe last updated on 24/Apr/25

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