In one of my textbook example, after the summation result was given, they simplified the expression but I can't see how this simplification was done.

$\displaystyle 0.5^k\left[\frac{1-(0.8/0.5)^{k+1}}{1-(0.8/0.5)}\right]=\frac{10}{3}[0.8^{k+1}-0.5^{k+1}]$

I don't see how the LHS simplified to the RHS? All help will be appreciated. Thanks in advance.