[Math] Find the sum of the geometric series: $\;\sum_{k = 4}^\infty \frac 2{3^k}$

Question

Find the sum of the geometric series: $\quad \displaystyle \sum_{k = 4}^\infty \frac 2{3^k}$

I converted $\dfrac{2}{(3^k)}$ into $2(3^{-k})$ so since $|r|>1$ the series diverges so I can't find a sum.

What am I doing wrong?

Answer 1

This is a geometric progression with first term $\frac{2}{3^4}$ and common ratio $\frac{1}{3}$. Now simply apply the formula for such series.