$\sum\limits_{n=0}^{1000000}\binom{2000000}{2n}\cdot{p}^{2n}\cdot(1-p)^{2000000-2n}$

Question

$\sum\limits_{n=0}^{1000000}\binom{2000000}{2n}\cdot{p}^{2n}\cdot(1-p)^{2000000-2n}$

How can I go about finding the above sum?

Thank you.

Answer 1

$$2\sum_{n=0}^{[r/2]}\binom r{2n}a^{2n}b^{r-2n}=(a+b)^r+(a-b)^r$$