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Null sequence question

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:

(edited 12 years ago)

Reply 1

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

Reply 2

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*

Reply 3

mootasaurous

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?

Reply 4

mootasaurous

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

Reply 5

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].

Reply 6

mootasaurous

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

Reply 7

gff

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?

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.