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95/1000, Most calculus 2 students get stuck on this infinite series! Series of ln(n)/n^2

• bprp calculus b… 오래 전 2026.08.10 16:00 인기
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@vikramrawat526… 　오래 전

Day 95

2026-08-10 19:10

[ytcid:Ugzel1sXkqDzRlY_iEZ4AaABAg] Day 95



@davidgillies62… 　오래 전

The solution involves zeta(2), the Euler-Mascheroni constant and Glaisher's constant. I have no idea how to go about proving this

2026-08-11 05:28

[ytcid:UgwaFb5O5YdibstTh214AaABAg] The solution involves zeta(2), the Euler-Mascheroni constant and Glaisher's constant. I have no idea how to go about proving this



@bit123taisao 　오래 전

Interesting: 0 < ε (infinitesimal) < r (any positive real number) < ∞
                    1 (x^0) < lnx < x^r (any positive real number) < e^x when x approaches ∞.

2026-08-10 21:35

[ytcid:UgxxhAC9BHT3oZbk4sx4AaABAg] Interesting: 0 < ε (infinitesimal) < r (any positive real number) < ∞ 1 (x^0) < lnx < x^r (any positive real number) < e^x when x approaches ∞.



@nathanellev311… 　오래 전

I solved it by integral test! I used IBP and learned that not only does it converge,but also converge to 1!

2026-08-10 20:26

[ytcid:Ugz0Vm8FMqIZN5OTU1Z4AaABAg] I solved it by integral test! I used IBP and learned that not only does it converge,but also converge to 1!



@sacha75019 　오래 전

≈0.93755 btw

2026-08-10 20:09

[ytcid:Ugz2vSw8jXbiV7llp-l4AaABAg] ≈0.93755 btw



@slavinojunepri… 　오래 전

Integral test works as well. Just prove the integral from 1 to infinity of ln(x)/x^2 exists to conclude the given series converge.

2026-08-10 17:23

[ytcid:UgxKtqSrGJWB6Y5XIjt4AaABAg] Integral test works as well. Just prove the integral from 1 to infinity of ln(x)/x^2 exists to conclude the given series converge.



@TannuBhardwaj-… 　오래 전

Day95?

2026-08-10 17:04

[ytcid:UgyiJMjIJQji5ECpB4J4AaABAg] Day95?



@TCARKofficial 　오래 전

Converges.

2026-08-10 16:13

[ytcid:UgwC0hfLDveNkT0G2XV4AaABAg] Converges.



@robloxcutter 　오래 전

converges obv

2026-08-10 16:12

[ytcid:Ugy490rP3CcFDESUmip4AaABAg] converges obv



@parkerschmitt1… 　오래 전

What does is exactly converge to? Could we use the zeta function?

2026-08-11 20:03

[ytcid:Ugx4G87VUl-p-Rc9qRh4AaABAg] What does is exactly converge to? Could we use the zeta function?



@ZeroContour 　오래 전

Use the series representation of zeta(s), and differentiate. Zeta'(2) has a closed form.

2026-08-12 04:32

[ytcid:Ugyk4ksmzs58I0lJk454AaABAg] Use the series representation of zeta(s), and differentiate. Zeta'(2) has a closed form.