Leibniz's Formula for Pi/Proof by Taylor Expansion

Proof
From Taylor Series Expansion for Arctangent Function, we obtain:


 * $\arctan x = x - \dfrac {x^3} 3 + \dfrac {x^5} 5 - \dfrac {x^7} 7 + \dfrac {x^9} 9 - \cdots$

Substituting $x = 1$ gives the required result.