Math undergrad.

Since $$\arctan (x)=\sum_{n=0}^{\infty}(-1)^n\frac{x^{2n+1}}{2n+1}$$ for $x\in[-1,1]$, when $x=1$, we have $$\frac\pi4=1-\frac13+\frac15-\frac17+\dots$$