Prove that the sum to `n` terms of the series `11+103+1005+ i s(10//9)(10^n-1)+n^2dot`

Explanation

To prove that the sum of the first \( n \) terms of the series \( 11 + 103 + 1005 + \ldots \) is given by the formula \( S_n = \frac{10}{9}(10^n - 1) + n^2 \), we will break down the series and analyze its components step by step.

### Step 1: Identify the Series
The series is:
\[ S_n = 11 + 103 + 1005 + \ldots \]
We can observe the terms and rewrite them in a more structured form:
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