It's also red, which means it's a debt. So it should be -1

What exactly is the question? Do you want to use the Euler-Lagrange method on ∑1/n^4?

Perhaps you mean that integral term at 32:23. Unfortunately, he simply drops this error term in the following. Doing it correctly, you can use this error term to calculate your accuracy. Peculiarly, this integral at 32:23 can be estimated by Bₘ* max[x=0..1] f⁽ᵐ⁾(x)/m! where m = k+1 if k is uneven. This formula relies on the fact that |Bₘ| ≥ |Bₘ(x)| for all even Bernoulli polynomials. To get an estimate for the error of the result of 48:22 of the Basel problem, we have to sum all these error terms up for all the intervals between the integers from 10 to ∞, for which we could use an integral once again. As 48:22 sums up to the 18th term, using B₁₈ as the last Bernoulli number, we use the 20th derivative of 1/x² for the error term: (1/x²)⁽²⁰⁾ = 21! / x²² The maximum of this function within an interval of ℝ⁺ is always on the lower bound of this interval. So we get: Error ≤ | B₂₀ / 20! * ∑ [k=10..∞] 21! / k²² | ≤ |B₂₀| * ( ∫ [x=10..∞] 21/ x²² dx + 1/2*21/10²² ) = |B₂₀| * 1/10²¹ * (1+21/20) = 174611/330 * 41/20 * 1/10²¹ < 1.085E-18 using the value of B₂₀ = -174611/330 of 35:30 in the video. Now the calculation of 48:22 gives Euler's result at 48:38: 1.644 934 066 848 226 436 95 ... while the true value of π²/6 is 1.644 934 066 848 226 436 47 ... so the true error is smaller than 5E-19. Which means that the above estimation of 1.085E-18 is quite a good one.