A robot's first step is 5 to the right, then it turns with an angle of $20°$ and its next step is $70\%$ of the length of the last. Where will the robot be after infinitely many steps?
Calculation: \begin{align} &z = 0,7(\cos(20°) + i\sin(20°))\\ &z_\infty = \frac{5}{1 - z} = 9.810 + 6.863i\\ & (9.810,6.863)\\ \end{align} But I don't get step 2. Can anyone explain this step to me?
Hint: $$\sum_{k=0}^\infty az^k=\frac{a}{1-z}.$$