How do you get to the stage where you can do this stuff?

>>8591550
>How do you get to the stage where you can do this stuff?

I genuinely dont intend to hurt your feelings or intelligence. But i learned how to do this type of problem in maybe 9th-10th grade. Although i would not be confident enough to say i know it for certain until 2nd year at uni.

>>8591556
To clarify, i did not understand the notation on the left at that grade, nor the inequality meaning in relation to the notation, but i would have been able to solve RHS at that age.

>>8591550
The way the problem is solved is voluntary hookus-pookus. With tools like ln you could find it more easily.

>>8591556
upboated

>>8591550
high-school?

>>8591599
You would have been able to the first line in High-School ?
The only thing I might have thought of would have been
1 < our number < (1 - 25/365)^25

And that's all. OIM (I'm assuming it is that) is hard.

>>8591609
You've studied in the US?

In education system (Germany) about in 11 grade with notation and all. Came up again in 1 semester in Uni again with a formal better approach

>>8591591
>voluntary hookus-pookus
...as opposed to involuntary hokus-pokus?

>>8591550

Don't worry.
It's a tool thing.
You know the inequalities or you don't.

>>8591550
After the first line it's not that hard, that said I'm not sure where that line comes from. I'd have to see the statement of the problem. However it has at least a passing similarity with to the arithmetic-geometric mean inequality, so maybe there's something there you could play with.

>>8591680
Actually it is the arithmetic-geometric mean inequality, my bad.

>>8591680

It is obviously AM-GM.
This sub is not for you.

>>8591811
Solid input senpai. I'm real glad you bumped this thread for that post.

>>8591625
No, but the curriculum wasn't about that sort of things. We learned derivatives, vectors, integrals, arithmetical and geometrical sequences. Not those inequalities.

>>8591550
There's a mistake in the 5th line

>>8591550
It's just basic algebra.
No need to learn spooky sums unless you need them. Boring stuff. Forget about them.

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>I have been doing these problems since I was 5 kid

>>8591550
The first line is AGM. The second line is arithmetic. The third line uses an inductive proof to simplify the arithmetic series, and uses arithmetic to simplify further. The fourth line elaborates the fraction into a binomial. The fifth line is a mistake, because line 6 assumes that (25*24/2)*(13/365)^2 is the intended term. Line 5 comes from expanding it into the binomial series, but removing every term after the first three. The inequality is correct because 13/365 is smaller than 1/28, which means the magnitude of each successive term of the sum will be smaller than the previous term (each binomial coefficient is produced by the running product 25/1 times 24/2 times 23/3 etc..., and the (13/365)^k term is produced by the running product (13/365) times (13/365) times (13/365) etc..., so the magnitude of the next term in the sum is smaller than the previous term). The first term removed is a negative term, so we can add it up with its positive successor, and do so with the rest of the terms (except -(13/365)^25, but it is negative anyway). These new terms are all negative, so we can cancel them all and say that (1 - 13/365)^25 < 1 - 25*13/365 + (25*24/2)*(13/365)^2. The rest of the lines are arithmetic simplification, but I have no idea how they figured out 2592/5329 < 1/2.

>>8591895
*The first line is the arithmetic-geometic inequality

>>8591895
1/2 = 2592/5184 > 2592/5329

>>8591556
He asked how you get there, not for your gloating

shitbag/10

OCD and Coffee works for me.

>>8591838
>>8591895

I don't know what are you smoking.
Everything looks fine.
Get out from this sub.

>>8591558
quality shitpost 9/10

[eqn]\Bigg[\frac{1}{25}\sum^{25}_{k=1}{\bigg(1-\frac{k}{365}\bigg)}\Bigg]^{25} \\ \Bigg[\frac{1}{25}\bigg(\sum^{25}_{k=1}{1}-\frac{1}{365}\sum^{25}_{k=1}{k}\bigg)\Bigg]^{25} \\ \Bigg[\frac{1}{25}\bigg(25-\frac{1}{365}\cdot \frac{25(25+1)}{2}\bigg)\Bigg]^{25}[/eqn]
and the rest is trivial.

>>8591550
could have just written a for loop.
that would have certainly been faster than all this shit

Aside from maybe some notation, this is easily within the reach of as HS Graduate

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lmao at the brainlets ITT
This was the first thing I did when I came out of the womb, I wrote this same equation with the afterbirth
lol give up now