Every Student Should See This

This has always been one of my absolute favorite visual proofs!

This sum 1 + 1/2 +1/3 +... is call the harmonic series. This is a great math proof showing why the harmonic series diverges! (We basically use the integral test for series)

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Prove It Like A Mathematician! (Intro To Math Proofs)

Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

#math #brithemathguy #shorts

[shinobix]

Infinity + infinity = infinity so I guess the answer is at least 2

[thatdudem]

Year 2, month 7, day 23: I'm starting to think this may be a loop

[piotrosiejuk]

More elegant proof:
1+
1/2+
1/3+1/4+ (sum of those 2 is larger than 1/2)
1/5+1/6+1/7+1/8 +(sum of those 4 is larger than 1/2)
...
You can keep on adding further "chains" (length 8, 16, 32 and so on), each with value of at least 1/2 (pretty obvious). This gives you an infinite number of 1/2s. This is infinity.

[quasarolive]

All infinities are great. But some infinities are greater than others.
- George Orwell

[SupremeST]

How many times are you gonna ask me bro😭😭i wanna go home

[cosinex]

In math, we have pretty much committed to memory: harmonic series always diverges

[HenrikhWolf]

No comment about the perfect loop?
whoa

[m.a]

+ You just can't add infinite numbers
- Hold my integral

[The_Honored_One_Inf]

For the next person to say the answer is ~2, that only applies to a sequence where the bottom number doubles every time. In this sequence it goes over two right after 1/3.

[ntlake]

Yes, and if you rotate that graph around the x-axis the volume will be π.
π ∫∞₁(1 / x²)dx =  π(−(1/∞)+ ‌1⁄1‌) =  π(0 + 1)  =  π

[Matthew_Klepadlo]

Ah yes, the endless truth of calculus: infinitely many things that are infinitely small giving you an exact solution to a problem…

[timm]

“put the excess area in a cap and call it Mascheroni”

[dannon]

“Just under two” me every time someone asks if I know my limit.

[TurkishKS]

If you change the series by rounding each fraction down to the nearest 1/x fraction, where x is a power of 2, you'll see that this series is the same as repeatedly adding 1/2 (per the grouping in brackets I've made below). Since this clearly smaller series, can be shown to be equivalent to repeatedly adding 1/2, and thus equal to infinity, the original larger series must be infinity as well.

1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 +1/8) + (1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16 + 1/16) + ...

[commy]

No calculus needed. Group up the terms like this: the first term, then the second, then the next 2, then the next 4, then the next 8. The first is greater than 1/2. The second is greater than 1/2. The next 2 are each greater than 1/4, so their sum is greater than 1/2. The next 4 are each greater than 1/8, so their sum is greater than 1/2. The next 8 are each greater than 1/16, so their sum is greater than 1/2, and so on... You get the sum of infinitely many times 1/2 which is infinity

[MistahPhone]

Another good explanation for this problem is this:
Take this equation, for example
X = 1/9 + 1/10 + 1/11 1/16
All of these are greater than or equal to 1/16, so let's just say x = 1/2 for demonstration purposes
Repeat this with 1/17...1/32, 1/33...1/64, and so on to get infinity because ½ × infinity is still infinity
Sorry if that didn't make sense

[starplayzreadbio]

That one math teacher who doesn't leave you until you get the answer:

[PepeChess-vhef]

It's called harmonic series and with n approaching infinity the sum will also be infinite. You can find a nice proof of it on wikipedia

[zpxnrmf]

integral of 1/x = ln|X|=> which means that as x tends to infinity, the limit will also be infinity

[Laittth]

crazy how the format of this video made the loop so seamless!!