Question

Determine if the series

2 +2/10 +2/100 +2/1000 +2/10,000 + ⋯
Is it convergent or divergent, if it is convergent, calculate the sum.

Answer 1

This is a convergent series with first term 2 and common ratio 1/10. The sum of this series is

`(2)/(1 - (1)/(10) ) = (2)/( (9)/(10) ) = 2 * (10)/(9) = (20)/(9) = 2 (2)/(9)`