We know that $\displaystyle\frac{1}{1+x^2}=1-x^2+{{x}^{4}}-{{x}^{6}}+...$ for $x\in\left(-1,1\right)$. **Using this fact, find the function that corresponds to the following series.** $\displaystyle x-\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}-\frac{x^7}{7}+...$ [[☃ radio 1]]