/sci/ - Science & Math

>>11584925
Try proving some inequality of the form [math]\sum _{k = 2}^n \frac{1}{k^2} < 1 + f(n)[/math], then the induction step becomes [math]f(n) - f(n+1) > \frac{1}{(n+1)^2}[/math] or something similar enough (note: typos might have been made).
>how do I choose f(n)
Try random stuff like [math]( \frac{n}{n+1})^2[/math] until something works.