## Task 3 - 271223

a) For each natural number $n$, a function $f$ (with the domain of all real $x \neq 0$) is defined by

$$
f(x)=\sum_{k=0}^{n}(k-2) \cdot x^{k}
$$

Determine all natural numbers $n$ for which the function $f$ satisfies the equation $f(-1)=-f(1)$.

b) For each natural number $n$, a function $g$ (with the same domain) is defined by

$$
g(x)=\sum_{k=0}^{n} \frac{1}{3 k-2} \cdot x^{k}
$$

Investigate whether there exists a natural number $n$ for which the function $g$ satisfies the equation $g(-1)=-g(1)$.