Power Series Representation

Find the power series representation for each of the following functions. Include the interval of convergence.

  1. \(\displaystyle{f(x)= \frac{2}{1+x}}\) Solution ↗
  2. \(\displaystyle{f(x)= \frac{3}{2-x}}\) Solution ↗
  3. \(\displaystyle{f(x)= \frac{x}{1-2x}}\) Solution ↗
  4. \(\displaystyle{ f(x)=\frac{5x}{x^2+4}}\) Solution ↗
  5. \(\displaystyle{f(x)=\frac{1+x}{1-x}}\) Solution ↗
  6. \(\displaystyle{ f(x)=\frac{1}{(1-x)^2}}\) Solution ↗
  7. \(\displaystyle{ f(x)= \frac{x}{(1+x)^2}} \) Solution ↗
  8. \(\displaystyle{f(x)=\frac{x}{(1+9x)^2}}\) (Solution coming soon)
  9. \(\displaystyle{ f(x)= x^2 \tan^{-1} x} \) Solution ↗
  10. \(\displaystyle{ f(x)= \frac{\tan^{-1} (2x)}{x^2}} \) Solution ↗
  11. \(\displaystyle{ f(x)=\ln(5-x)}\) Solution ↗
  12. \(\displaystyle{f(x)=\ln(2+x)}\) Solution ↗
  13. \(\displaystyle{ f(x)=\ln|2+3x|}\) Solution ↗ Alt Solution ↗