Infinite Sum of a Converging Series of Inverse Cosines

66 Views Asked by At

I was wondering if anyone knew a way to find the value of d for the following converging infinite sum:

$$ \sum_{n=2 }^{\infty}\arccos \left ( -\frac{d^{n+1}+d^{2n}+d^n-d}{(d^{n-1}-1)(d^n-d)} \right ) = \pi $$

Thanks!