Find the sum of \(n\) terms of the geometric progression \[\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\dotsb.\] [If a general formula is used, it must first be proved.]

Deduce the sum to infinity of this series.

Find the least number of terms of the series which must be taken for their sum to exceed \(\dfrac{2999}{4000}\).