Basel problem

[Qanon No.14562537]

Is this formula true?

[Anonymous No.14562546]

What do the experts say? Always believe the opposite of what the experts say

[Anonymous No.14562558]

>>14562537
It's an empirically verifiable proposition. You can literally take the first few digits of pi, square it, divide by 6, and compare it with the first few terms of the sum. You'll see that they close. You can even get exact estimates by noting that
[math]\sum_{n=N+1}^\infty \frac{1}{n^2} \leq \int_N^\infty dx/x^2 = 1/N[/math]

[harry No.14562564]

Ἀριστοτέλης

[Anonymous No.14563417]

>>14562564
Can I get a quick rundown on why this faggot keeps posting variations of this trivial limit? He doesn't actually think he's on to something does he?

[Anonymous No.14563450]

>>14562558
>compare it with the first few terms of the sum
that sum converges famously slowly. you need a quintillion terms to get even 20 digits of pi.

[pepe No.14563623]

lie?

[Anonymous No.14563651]

>>14562537
Yes. I proved it in undergrad but don't remember details anymore. The proof for 1/n^4 is fun too

[Anonymous No.14563658]

Why do so many people deny proofs?

[Anonymous No.14563669]

>>14563658
Fuck showing your work? Cheaters take credit?

[Anonymous No.14563672]

>>14562537
>Basel problem
moar liek Based problem AMIRITE

[Anonymous No.14563695]

>>14563450
Use eta function series acceleration for fast convergence of zeta.
eta and zeta are related by functional equation and there are very fast ways to compute eta.

[Anonymous No.14563730]

>>14562537
Yes, it is.

[Anonymous No.14564342]

>>14562558
>empirically verifiable
>exact estimates
calculus has rotted your brain