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Please help me find a formula for the $a_n$ in this sequence, $$ 1,\, \frac{1}{2\sqrt 2},\, \frac{1}{3\sqrt 3},\, \ldots $$

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What do you think the next three terms are? –  Jonas Meyer Oct 2 '12 at 6:22
@JonasMeyer I have thought about it for a while now, I have no clue, tell me please. –  AD. Oct 13 '12 at 12:59
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2 Answers

up vote 1 down vote accepted


$a_1=1=\frac{1}{1\sqrt 1}$,

$a_2=\frac{1}{2\sqrt 2}$,

$a_3=\frac{1}{3\sqrt 3}$,


$a_n=\frac{1}{n\sqrt n}$.

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With this sort of problem, you really only have to come up with some sort of pattern or closed form that fits/describes what you've got so far. There could be many viable patterns--some far more obvious than others--but whatever you pick, you should be fine as long as you can justify it.

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