/sci/ - Science & Math

[Anonymous No.9894941]

How many engineers and CS majors actually end up doing research/helping build something innovative like aerospace, stem cells etc. versus just optimizing on mundane stuff that already exists like creating more efficient laundry detergent manufacturing or server work on a quirky two syllable app that will fail in two months.

[Anonymous No.9894961]

>>9894941
The solution to that problem has not yet been discovered. Maybe someday, with future advancements, we will be able to figure the answer, but as of right now, no one alive can conclusively say whether or not it converges.

[Anonymous No.9894986]

>>9894961
But the picture says you should be able to solve it, why would Kurisu lie.

[Anonymous No.9895201]

How many researchers and academics actually end up doing research/helping build something innovative like aerospace, stem cells etc. versus just reproducing mundane stuff that was already done like collecting data from cancer cells in petri dishes or publishing surveys on the stability of same-sex-parent families in which everything is self-reported.

[Anonymous No.9895588]

>>9894941
studied mech. engineering for 5 years, got masters, cant find any job because they all want 2047 years experience which i cant have if nobody takes me, tried going to interviews in person to 2 local firms, one afterwards sent me a letter saying that theyre not hiring atm (they were) and the other politely told me to fuck off.
since about 2 years i now work as a car mechanic with cool slavs and i regret nothing
maybe i will eventually try getting a real job with the degree in some other country because germany is a shithole when it comes to STEM jobs but for now i am more than fine with my situation

[Anonymous No.9896370]

>>9894961
Why doesn't it converge though? Surely it does due to the alternating series test?

[Anonymous No.9896374]

>>9896370
>alternating series
>all terms are positive

[Anonymous No.9896375]

>>9896374
Fuck didn't see the squared term sorry

[Anonymous No.9896377]

>>9896374
It could be simplified to 1/(sin x)^2 though since the 1/n^3 term multiplied in would make it smaller, so if that converges we're good right?

[Anonymous No.9896381]

>>9896377
1/(sin(x)^2) obviously doesn't converge

[Anonymous No.9896390]

>>9896381
I understand that 1/sin^2 x (csc^2 x) doesn't converge but why not 1/(sin x ^2)?

[Anonymous No.9896394]

>>9896390
You mean the sum of 1/sin(x^2) ?

[Anonymous No.9896399]

>>9896390
sin^2(x) = (sin x)^2

sin(x^2) is another function altogether.

Also note that none of these functions (or their reciprocals) converge nor do their sums.

[Anonymous No.9896408]

>>9896390
For starters, 1/sin^2(n) is always > 1, so it can't even approach 0 as n - > infinity

[Anonymous No.9896410]

>>9896399
>>9896394
sin x = x - x^3/3! + x^5/5! ....
(sin x)^2 = x^2 + (x^3/3!)^2 +(x^5/5!)^2....
gets large very fast towards infinity
however when flipped (1/n), shouldn't this approach zero? Since all the terms individually would reach zero? i.e. 1/x^2 + 1/(x^3/3!) +1/(x^5/5!)....

[Anonymous No.9896417]

>>9896410
I meant squared terms on the last two terms. I guess the only concern would be the speed of growth of (2n-1)! but wolfram alpha seems to concur with my intuition here. Why does this diverge?

[Anonymous No.9896428]

>>9896417
>>9896410
Wait sorry im an idiot. (a+b)^2 != a^2+b^2.
Polite sage.

[Anonymous No.9896460]

>>9896428
>>9896410
Also note that even if each term goes to zero individually, the infinite sum might not go to zero (it could, but that would require some proof). In general, we don't know if (limit of sum) = (sum of limits) for infinite sums.

I don't have my copy of "Counterexamples in Analysis" on hand but it (or really any real analysis text) has a specific example where (limit of sum) =/= (sum of limits).

[Anonymous No.9896574]

anon, innovating involves making things more efficient and easier to use. Stem cell / aerospace researchers do a hella lotta that.

[Anonymous No.9896746]

>>9894941
quite a lot however they dont innovate much in their field, instead they collaborate with other fields

[Anonymous No.9897039]

>>9894941
It's a divergent series as every so often the sin(n) values are zero.
You can't even say it's conditionally convergent as you'd have to be able to remove a finite number of terms but the terms you'd have to remove to union would be infinite as well.

[Anonymous No.9897192]

>>9894941
sin(n)^2 can get arbitrarily close to 0 so the whole term can get arbitrarily close to infinity

[Anonymous No.9897242]

>>9894941
I solved it :^)