The sequence $\{a_n\}$ satisfies the following for all natural numbers $n$: $$\sum_{k=1}^{n} a_k = \log \frac{(n+1)(n+2)}{2}$$ Let $\sum_{k=1}^{20} a_{2k} = p$. Find the value of $10^p$. [4 points]
The sequence $\{a_n\}$ satisfies the following for all natural numbers $n$:
$$\sum_{k=1}^{n} a_k = \log \frac{(n+1)(n+2)}{2}$$
Let $\sum_{k=1}^{20} a_{2k} = p$. Find the value of $10^p$. [4 points]