Does the Series converge? If so, find the sum

The series given in the problem is `sum_(n=1)^oo 2/10^n` .

This is a convergent series. It is a geometric series with first term `2/10` and common ratio `1/10` .

The sum of

`sum_(n=1)^oo 2/10^n `

= `(2/10)/(1 - 1/10)`

= `(2/10)/(9/10)`

= `2/9`

The required sum `sum_(n=1)^oo 2/10^n = 2/9`

Comments

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