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 series \(11 + 103 + 1005 + \ldots\) up to \(n\) terms is given by the formula \(\frac{10}{9}(10^n - 1) + n^2\), we can follow these steps:

### Step 1: Identify the Pattern in the Series
The series consists of the terms:
- \(11 = 10^1 + 1\)
- \(103 = 10^2 + 3\)
- \(1005 = 10^3 + 5\)

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