Comparing Two Sums with Binomial Coefficients How do I use pascals identity:
$${2n\choose 2k}={2n-1\choose 2k}+{2n-1\choose 2k-1}$$ to prove that
$$\displaystyle\sum_{k=0}^{n}{2n\choose 2k}=\displaystyle\sum_{k=0}^{2n-1}{2n-1\choose k}$$
for every positive integer $n$ ?

HINT
Write out what you want to prove for $n = 1$ and $n = 2$. Use Pascal's identity. If you are stuck after this, update your question with your work and we'll go from there.
