Evaluate `S=sum_(n=0)^n(2^n)/((a^(2^n)+1)` (where `a>1)`.

Explanation

To evaluate the sum \( S = \sum_{n=0}^{\infty} \frac{2^n}{a^{2^n} + 1} \) where \( a > 1 \), we will follow these steps:

### Step 1: Write the Series
We start with the series:
\[ S = \sum_{n=0}^{\infty} \frac{2^n}{a^{2^n} + 1} \]

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