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Determine Whether the Series 81100+9101+109- \frac { 81 } { 100 } + \frac { 9 } { 10 } - 1 + \frac { 10 } { 9 } - \ldots

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Determine whether the series 81100+9101+109- \frac { 81 } { 100 } + \frac { 9 } { 10 } - 1 + \frac { 10 } { 9 } - \ldots is convergent or divergent. If it is convergent, find its sum.

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