Oh,Oh,Oh,merry analysis!!!

bobbym · 2012-03-09 07:15:51

Hmmmm. That is a good question. I really do not know the answer to that.

anonimnystefy · 2012-03-09 07:38:00

hi bobbym

than what should be the coefficient of x^10?

bobbym · 2012-03-09 07:39:58

That was my original question. What is the coefficient of x^10? Then I asked whether you knew how to get it.

anonimnystefy · 2012-03-09 07:42:17

hi bobbym

it's 105,if the given sequence is the Tribonacci sequence.

bobbym · 2012-03-09 07:49:34

Hi;

We seem to have this difficulty in thought. You are making a statement "this implies that." I on the other hand attach very little weight to those type statements. My method is to look. I never trust reasoning over experimentation or observation. Only when I have no choice.

Now, again I must say that is not the coefficient of x^10 in your GF.

anonimnystefy · 2012-03-09 07:55:30

can you explain how it isn't because when i expand that i get 105.

bobbym · 2012-03-09 07:57:38

I do not agree. When and where did you expand it?

anonimnystefy · 2012-03-09 08:01:09

i expanded it using wolfram.

bobbym · 2012-03-09 08:04:47

Hmmmm?

anonimnystefy · 2012-03-09 08:11:00

hi bobbym

i just seen the nine as ten.but the GF is still correct.i took a0=1,a1=1,a2=1.

bobbym · 2012-03-09 08:16:35

Hi;

That is because you went back to the "this implies that" reasoning you have been taught.

The question I was asking has nothing really to do with the Tribonacci numbers. I was asking for you to look at the x^10 coefficient.

anonimnystefy · 2012-03-09 08:19:01

hi bobbym

my x^10 term has the coefficient 193.

bobbym · 2012-03-09 08:24:19

Very good. So you have some experimental verification of your original gf.

anonimnystefy · 2012-03-09 09:06:52

hi bobbym

yes i do.

bobbym · 2012-03-09 09:09:15

So, what about this problem?

If I wanted to get e^.51 to 500 digits of accuracy how many terms of its Mclaurin series are necessary?

anonimnystefy · 2012-03-09 09:15:21

hi bobbym

i will do it tomorrow.i have to go sleep now because i'm waking up at 6.30 tomorrow.

bobbym · 2012-03-09 09:16:08

Oh, okay get some rest. I will see you tomorrow.

anonimnystefy · 2012-03-10 08:18:27

hi bobbym

i forgot how to do this a little.

if i take the mclaurin's expansion of e^x i get

the general term of the above sequence is

i'm not writing this using the Big Oh notation yet because i don't know what terms i need.

now,because we are needed to get the first 500 digits correct,this means that the sum of first n terms must differ from the above sequence for at most 10^(-501)

so if i take the first n terms which go up to x^(n-1)/(n-1)! the difference of that sum and the mclaurin's series for e^x should differ for at most 10^(-501).

so:

so (0.51)^n must be less than or equal to 10^(-501).

we solve the inequality:

we solve for n and get the smallest integer value the falls into the interval we got by solving,which is 1714.

something seems wrong here,but not if it really is and if it is then where.

Last edited by anonimnystefy (2012-03-10 08:19:57)

bobbym · 2012-03-10 10:14:25

Hi anonimnystefy;

That answer is of course too large.

anonimnystefy · 2012-03-10 10:48:57

Hi bobbym

Obviously, but I don't know what's wrong with it.

bobbym · 2012-03-10 11:15:52

It is too generous. There are two ways to bound the error. They both give a maximum of 236 terms or less.

anonimnystefy · 2012-03-10 11:18:27

And those are?

bobbym · 2012-03-10 11:40:01

Geometric series and the taylor remainder.

anonimnystefy · 2012-03-11 09:07:56

hi bobbym

the taylor remainder.is that what we did earlier with the principal part?

bobbym · 2012-03-11 10:35:54

Try the geometric one first. The Taylor remainder is just an expression.

Math Is Fun Forum

#426 2012-03-09 07:15:51

Re: Oh,Oh,Oh,merry analysis!!!

#427 2012-03-09 07:38:00

Re: Oh,Oh,Oh,merry analysis!!!

#428 2012-03-09 07:39:58

Re: Oh,Oh,Oh,merry analysis!!!

#429 2012-03-09 07:42:17

Re: Oh,Oh,Oh,merry analysis!!!

#430 2012-03-09 07:49:34

Re: Oh,Oh,Oh,merry analysis!!!

#431 2012-03-09 07:55:30

Re: Oh,Oh,Oh,merry analysis!!!

#432 2012-03-09 07:57:38

Re: Oh,Oh,Oh,merry analysis!!!

#433 2012-03-09 08:01:09

Re: Oh,Oh,Oh,merry analysis!!!

#434 2012-03-09 08:04:47

Re: Oh,Oh,Oh,merry analysis!!!

#435 2012-03-09 08:11:00

Re: Oh,Oh,Oh,merry analysis!!!

#436 2012-03-09 08:16:35

Re: Oh,Oh,Oh,merry analysis!!!

#437 2012-03-09 08:19:01

Re: Oh,Oh,Oh,merry analysis!!!

#438 2012-03-09 08:24:19

Re: Oh,Oh,Oh,merry analysis!!!

#439 2012-03-09 09:06:52

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#440 2012-03-09 09:09:15

Re: Oh,Oh,Oh,merry analysis!!!

#441 2012-03-09 09:15:21

Re: Oh,Oh,Oh,merry analysis!!!

#442 2012-03-09 09:16:08

Re: Oh,Oh,Oh,merry analysis!!!

#443 2012-03-10 08:18:27

Re: Oh,Oh,Oh,merry analysis!!!

#444 2012-03-10 10:14:25

Re: Oh,Oh,Oh,merry analysis!!!

#445 2012-03-10 10:48:57

Re: Oh,Oh,Oh,merry analysis!!!

#446 2012-03-10 11:15:52

Re: Oh,Oh,Oh,merry analysis!!!

#447 2012-03-10 11:18:27

Re: Oh,Oh,Oh,merry analysis!!!

#448 2012-03-10 11:40:01

Re: Oh,Oh,Oh,merry analysis!!!

#449 2012-03-11 09:07:56

Re: Oh,Oh,Oh,merry analysis!!!

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Re: Oh,Oh,Oh,merry analysis!!!

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