Null sequence question

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mootasaurous
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#1
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#1
I'm stuck on an annoyingly easy question about null sequences. :ashamed2:

Use the list of basic null sequences and the various rules to prove the following sequence is null:

{ (n^10 x 10^n) / n! }

basic null sequences are:
{1/n^p} p>0
{c^n} |c|<1
{n^p x c^n} p>0, |c|<1
{c^n/n!}
{n^p/n!} p>0

and the various rules are sum rule, product rule, multiple rule.

thanks!! :ahee:
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gff
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#2
Report 10 years ago
#2
What about focusing on one of the sequences in this list, and using a bit of common sense about n^{10} and 10^n?
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sputum
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#3
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#3
split off half the numerator, prove the remainder is null and use the multiple rule to show any multiple of the bit you cut off by a null sequence is null?

*crosses fingers*
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mootasaurous
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#4
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#4
(Original post by gff)
What about focusing on one of the sequences in this list, and using a bit of common sense about n^{10} and 10^n?
I've been trying to do that, im not quite sure what you mean about common sense about n^10 and 10^n?
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mootasaurous
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#5
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#5
(Original post by sputum)
split off half the numerator, prove the remainder is null and use the multiple rule to show any multiple of the bit you cut off by a null sequence is null?

*crosses fingers*
I thought about that but according to the multiple rule, the multiplier has to be a real number (i think?) and it wouldnt be multiplying it by a real number, it would be either n^10 or 10^n

or am i being silly
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DFranklin
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#6
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#6
What are the "various rules" here? [I'm treating this as an exercise in "proof using only these facts", in which case we need to know what facts we can assume].
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mootasaurous
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#7
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#7
(Original post by DFranklin)
What are the "various rules" here? [I'm treating this as an exercise in "proof using only these facts", in which case we need to know what facts we can assume].
If {a} and {b} are null then
{a+b} is null - sum rule
{Ka} is null, K belongs to all real numbers - multiple rule
{ab} is null - product rule
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gff
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#8
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#8
(Original post by mootasaurous)
I've been trying to do that, im not quite sure what you mean about common sense about n^10 and 10^n?
As n gets bigger, which of the two things has the greatest value?
Hence, can you find something that is bigger than your sequence at some point, and is still a null one.

EDIT: I guess this may not be the best advice, given that you need to only use rules.
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DFranklin
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#9
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#9
(Original post by mootasaurous)
If {a} and {b} are null then
{a+b} is null - sum rule
{Ka} is null, K belongs to all real numbers - multiple rule
{ab} is null - product rule
I don't see how to do it using only those rules.

Edit: the "best" I can see requires also: if {a^2} is null than {a} is null.
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sputum
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#10
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#10
(Original post by mootasaurous)
I thought about that but according to the multiple rule, the multiplier has to be a real number (i think?) and it wouldnt be multiplying it by a real number, it would be either n^10 or 10^n

or am i being silly
No, I think I was.

10n dominates n10 so you could squeeze it between 2*10n and something maybe?
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DFranklin
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#11
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#11
(Original post by sputum)
..
Squeezing isn't one of the "rules" though.

Idea is good though.

Following through: n^10/10^n is null, and 100^n/n! is null, so...
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sputum
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#12
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#12
(Original post by DFranklin)
I don't see how to do it using only those rules.

Edit: the "best" I can see requires also: if {a^2} is null than {a} is null.
is this not the product rule?
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mootasaurous
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#13
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#13
(Original post by DFranklin)
Squeezing isn't one of the "rules" though.

Idea is good though.

Following through: n^10/10^n is null, and 100^n/n! is null, so...
oooh! i think you've got it!

thanks for helping everyone
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Totally Tom
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#14
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#14
"postgraduate"?
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mootasaurous
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#15
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#15
(Original post by Totally Tom)
"postgraduate"?
oh oops
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dlynton
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#16
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#16
N
(Original post by DFranklin)
Squeezing isn't one of the "rules" though.

Idea is good though.

Following through: n^10/10^n is null, and 100^n/n! is null, so...
10^n*10^n is not 100^n its 10^2n
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DFranklin
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#17
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#17
(Original post by dlynton)
N

10^n*10^n is not 100^n its 10^2n
No. 10^n * 10^n = 100^n = 10^2n.
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Solz92
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#18
Report 7 years ago
#18
Is {2/n!} a null sequence
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