## 38. Simone and Her Complexes

Simone suffered from numerous complexes. Therefore, she decided to go to one psychoanalyst and after a course of treatment, she got rid of half of her complexes and half of one of the remaining complexes. Then she went to another psychoanalyst, thanks to which she got rid of half of the remaining complexes and half of one of the still remaining complexes. The result of her visit to the third psychoanalyst was exactly the same. After this, Simone was left with only one complex, from which she will not part until the end of her days.

How much did Simone's treatment cost, assuming that each psychoanalyst charged 197 francs for each cured complex?
38. Consider the following table:

| Stage of Treatment | Number of Complexes |
| :--- | :---: |
|  | 1 |
| At the end | $(1+1 / 2) \cdot 2=3$ |
| Before the 3rd psychoanalyst | $(3+1 / 2) \cdot 2=7$ |
| Before the 2nd psychoanalyst | $(7+1 / 2) \cdot 2=15$ |
| Before the 1st psychoanalyst | $(7+1)$ |

Thus, at the beginning, Simone suffered from 15 complexes. For the entire treatment, she had to pay

$$
14 \cdot 197=2758 \text { francs. }
$$