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Explicit Formula


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My math teacher got pissed (exaggeration she was just disappointed and left us work on number sets) because no one in the class knew what she meant when she asked what N meant in "n is an element of N". Which was part of the definition of explicit formula. I figure after looking at number sets she meant Natural numbers, but then we have examples with sequences that start at 0 or in the negatives. This lesson was intro to sequences. The explicit formula definiton was under definition part of the note (first part) and then the examples were under another subtitle called Arithmetic sequences. So was the explicit formula for another type of sequence or is it directly related? And is "N" natural numbers?

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You are right in saying that "N" means natural numbers. This makes sense since you never have a 1.5 term or a 1/4 term, you have the 1st term, 2nd term, 3rd term, and so on. When we did this stuff, we always started at n=1 and went on from there... As for this "explicit formula" stuff, I'm not sure what you're talking about. If it was tn=t1+(n-1)d then that is the formula for finding the nth term of an arithmetic sequence. If not, then please post it if you have questions.

Hope this helps (its been a very long time so some of this stuff might not be very clear)! smile.gif

Edited by Fire Emblem Addict
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You are right in saying that "N" means natural numbers. This makes sense since you never have a 1.5 term or a 1/4 term, you have the 1st term, 2nd term, 3rd term, and so on. When we did this stuff, we always started at n=1 and went on from there... As for this "explicit formula" stuff, I'm not sure what you're talking about. If it was tn=t1+(n-1)d then that is the formula for finding the nth term of an arithmetic sequence. If not, then please post it if you have questions.

Hope this helps (its been a very long time so some of this stuff might not be very clear)! smile.gif

Yeah that is the formula. Thanks, I was thinking of n as the sequence of numbers, not the term numbers.

Edited by Jhen Mohran
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My math teacher got pissed (exaggeration she was just disappointed and left us work on number sets) because no one in the class knew what she meant when she asked what N meant in "n is an element of N". Which was part of the definition of explicit formula. I figure after looking at number sets she meant Natural numbers, but then we have examples with sequences that start at 0 or in the negatives. This lesson was intro to sequences. The explicit formula definiton was under definition part of the note (first part) and then the examples were under another subtitle called Arithmetic sequences. So was the explicit formula for another type of sequence or is it directly related? And is "N" natural numbers?

Explicit formula is only contrasted with Recursive formula, as I remember it. I see no reason why it would necessarily be tied to the Natural numbers, or even the non-negative integers. I could imagine sequence definitions being formed using any basis set that is bounded on at least one end.

Also, to keep your teacher from being pissed again, remember Z means integers.

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that's not how erotic material works

Then you are naive. Mathematical porn may seem strange to those who have not aquired a taste for it, however, once one experiences the pleasures of mathematical reasoning, one will never find a more pleasureable activity than solving mathematical problems. So here's my advice, next time you're doing math problems, don't just do it mechanically. You must FEEL the math in order to experience the world of infinite pleasures (much like music). Once you know the joy and pleasure of mathematics, you will never go back to conventional porn again. I promise!

NOTE: Since you are new to this and math porn is an aquired taste, be sure not to start off with the hardcore stuff (integral calculus, topology, etc.) but rather start with something easy, like solving a simple quadratic or exponential equation (analogous to softcore porn). Once you have experienced that, you may move onto the more advanced stuff (analogous to hardcore porn). There also exist many "fetishes" such as applied mathematics that you may want to get into once you familiarize yourself with the basics. Happy MATHturbating!

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Explicit formula is only contrasted with Recursive formula, as I remember it. I see no reason why it would necessarily be tied to the Natural numbers, or even the non-negative integers. I could imagine sequence definitions being formed using any basis set that is bounded on at least one end.

Also, to keep your teacher from being pissed again, remember Z means integers.

n in this case is the term number. Therefore, n=1 is the first term, n=2 is the second term, etc. It would not make sense to have a -1st term or a 3.587th term.

Edited by Fire Emblem Addict
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You've never seen a sequence start at a0?

Well when we did this, we always started at n=1. We have to if the formula tn=t1+(n-1)d is to work. If we started at n=0, then tn=t0+(n-1)d does not make sense since for n=0 since it would only hold true if d=0. But I am aware that there are different conventions for doing this.

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while (true) {
       member.fill(/*( . )( . )
                       )    (
                      (  ()  )
                    */orifice);
       member.remove();
       if (!member.soften() && member.tumescence() > ORGASM) {
               member.splooge();
               member.soften(true);
       }
       if (member.soft()) break;
}

much better.

fucking nerd~

Edited by Obviam
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while (true) {
       member.fill(/*( . )( . )
                       )    (
                  	(  ()  )
                	*/orifice);
       member.remove();
       if (!member.soften() && member.tumescence() > ORGASM) {
               member.splooge();
               member.soften(true);
       }
       if (member.soft()) break;
}

much better.

fucking nerd~

Program scripts just don't turn me on for some reason.... But if you think that's hot, try drawing erotic images on your graphing calculator. Mmmmmm.... wink.gif

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I don't think that made any sense.

Couse it does! I'm just pointing out that there is something waaaay better than erotic programming out there in the realm of mathematics! Anyways, at least TRY a bit of math porn before you dismiss it please.... I promise that it is worth it!

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OK, before anyone judges or think less of me, please note that what I said in this thread was a joke (except for the parts that are relevant to the question). Just wanted to get that out there before anyone thinks that I'm sick..

Oh, and I actually hate math BTW

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No, nothing you said made sense.

Program scripts

These words do not go together in this context and they actually clash super fucking hard. It hurts my eyes to read this.

just don't turn me on for some reason....

What the fuck is wrong with you.

But if you think that's hot, try drawing erotic images on your graphing calculator. Mmmmmm.... wink.gif

Yeah, let me tell you 'bout how fucking hot that makes me. Fullcolor 72dpi or gtfo.

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I will concede that I perhaps used the wrong technical terminology.

Yeah, let me tell you 'bout how fucking hot that makes me. Fullcolor 72dpi or gtfo.

This is like judging a video game solely on its graphics....

With this, you are neglecting the artistic value of the material. Photo realism isn't always the best form of art. There's other (more abstract) kinds of art that are also very good

Edited by Fire Emblem Addict
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Should've posted this in General if you didn't want shit posted in your thread.

And in this case, porn.

I like porn.

I like math porn. But not this math porn. What the fuck are you talking about?

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