Prove that ` sum_(k=0)^(9) x^(k)"divides" sum_(k=0)^(9) x^(kkkk)`

Explanation

To prove that \( \sum_{k=0}^{9} x^{k} \) divides \( \sum_{k=0}^{9} k^{k} x^{k} \), we can follow these steps:

### Step 1: Define the Sums
Let:
- \( S_1 = \sum_{k=0}^{9} k^{k} x^{k} \)
- \( S_2 = \sum_{k=0}^{9} x^{k} \)

### Step 2: Calculate \( S_2 \)
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