Find the sum to infinity of the series .
`(i) 1+ (2)/(11) + (3)/(121) + (4)/(1331) + … + n((1)/(11))^(n-1) + … `
(ii) ` 1 + (4)/(7) + (9)/(49) + (16) / (343) +…+ n^(2) ((1)/(7))^(n-1) +…`

Explanation

To find the sum to infinity of the given series, we will analyze each part step by step.

### Part (i)

The series is given as:
\[ S = 1 + \frac{2}{11} + \frac{3}{121} + \frac{4}{1331} + \ldots + n \left( \frac{1}{11} \right)^{n-1} + \ldots \]

1. **Identify the general term**: The general term can be expressed as:
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