The Maclaurin series for arctan(x)\arctan(x)arctan(x) is arctan(x)=∑n=0∞(−1)nx2n+12n+1for ∣x∣≤1\arctan(x) = \sum_{n=0}^{\infty} \frac{(-1)^n x^{2n+1}}{2n+1} \quad \text{for } |x| \leq 1arctan(x)=∑n=0∞2n+1(−1)nx2n+1for ∣x∣≤1 Using this series, what is arctan(1)\arctan(1)arctan(1)?
π2\frac{\pi}{2}2π
π4\frac{\pi}{4}4π
π6\frac{\pi}{6}6π
π3\frac{\pi}{3}3π