OK, math geek

[petmoosie]

"

an infinite number of peptide hormones involved in the digestive system

The Math Geek Says: That's not possible. There'd have to be no upper bound on the number of atoms in the hormone. In a person who weighs, say, 100 kg, there are no more than 6.022*10²⁸ atoms (that's the number if they were all hydrogen atoms); and there can't be more atoms in the hormone than there are in the entire body.

Now, granted, the only upper bound I can place on the number of hormones (without knowing more about their structure) is (6.022*10²⁸)!, which certainly qualifies as Lots. But it's still finite. :-)" from metageek 's comment at least a year ago.

Possible hormones in the digestive system are peptide hormones so they are composed of any of 20 amino acids, in a chain of length 3 to 30 amino acids long. So a mathematical expression for that would be:

20^3 +20^4 +20^5 + ... + 20^30, where the ... is terms of 20^n for n=6 to 29.  Is there any compact way to express this? Is there a way of doing this in a shorter way?
 

Comments

Yes, and yes

[metageek.livejournal.com]

Let's see here...

N = ∑_{3 ≤ i ≤ 30} 20ⁱ

N = 20² ∑_{1 ≤ i ≤ 28} 20ⁱ

Now, the next step involves knowing that (x-1)(xⁿ + x^n-1 + … x¹ + 1) = xⁿ⁺¹-1. So we have:

N = 20² (20²⁹-1)/(20-1)

...which comes out to 11,302,545,200. Not even a trillion.

Re: Yes, and yes

[petmoosie.livejournal.com]

Thanks!!!

How did you get the summation sign? and the subscripts/superscripts to appear?

Don't be shocked if I tell you that the top number of amino acids is actually smaller than 30. There is a top number, but I don't actually know it. So, yeah, not even a trillion. But more than I can comfortably memorize.

Re: Yes, and yes

[metageek.livejournal.com]

How did you get the summation sign? and the subscripts/superscripts to appear?

Summation is just &sum; (see Character entity references in HTML 4, from the HTML spec); (sub|super)scripts are <sub> and <sup>, respectively.