This series can be rewritten as sum_{n=1}^\infty 2(2/5)^{n-1} and is thus a geometric series with first term 2 and common ratio 2/5. Since the common ratio is less than 1 (in absolute value), the series is convergent and its sum is given by "first term"/(1-"common ratio")=2/(1-2/5)=10/3. See Geometric Series